Solving the inverse Sturm–Liouville problem with singular potential and with polynomials in the boundary conditions
In this paper, we for the first time get constructive solution for the inverse Sturm–Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl functi...
Uloženo v:
| Vydáno v: | Analysis and mathematical physics Ročník 13; číslo 5 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.10.2023
|
| Témata: | |
| ISSN: | 1664-2368, 1664-235X |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | In this paper, we for the first time get constructive solution for the inverse Sturm–Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl function is proved. An algorithm of solving the inverse problem is obtained and justified. More concretely, we reduce the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences and then derive reconstruction formulas for the problem coefficients, which are new even for the case of regular potential. Note that the spectral problem in this paper is investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. In the future, our results can be applied to investigation of the inverse problem solvability and stability as well as to development of numerical methods for the reconstruction. |
|---|---|
| AbstractList | In this paper, we for the first time get constructive solution for the inverse Sturm–Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl function is proved. An algorithm of solving the inverse problem is obtained and justified. More concretely, we reduce the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences and then derive reconstruction formulas for the problem coefficients, which are new even for the case of regular potential. Note that the spectral problem in this paper is investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. In the future, our results can be applied to investigation of the inverse problem solvability and stability as well as to development of numerical methods for the reconstruction. |
| ArticleNumber | 79 |
| Author | Chitorkin, Egor E. Bondarenko, Natalia P. |
| Author_xml | – sequence: 1 givenname: Egor E. surname: Chitorkin fullname: Chitorkin, Egor E. email: chitorkin.ee@ssau.ru organization: Institute of IT and Cybernetics, Samara National Research University, Department of Mechanics and Mathematics, Saratov State University – sequence: 2 givenname: Natalia P. surname: Bondarenko fullname: Bondarenko, Natalia P. organization: Department of Mechanics and Mathematics, Saratov State University, Department of Applied Mathematics and Physics, Samara National Research University, Peoples’ Friendship University of Russia (RUDN University) |
| BookMark | eNp9kE1OwzAQhS1UJErpBVj5AgH_JE66RBV_UiUWBYmd5ThO68qxK9sp6o47cENOgtsgFiy6mRnZ73uaeZdgZJ1VAFxjdIMRKm8DppTkGSI0Q6jKi4yegTFmLM8ILd5HfzOrLsA0hA1CCOcFy1k5Bv3SmZ22KxjXCmq7Uz4ouIy9774_vxba9TttjIJb72qjOvih4xqGpO-N8HDrorJRCwOFbYa_rTN767r0FpLd0bV2vW2E30PpbKOjdjZcgfM2KdT0t0_A28P96_wpW7w8Ps_vFpkkMxwzQWuBq5LgFuOCsgalVpdYSYXbQs0aWqciWcHaQqIZbiuaU0TKmhGG2kZJOgHV4Cu9C8GrlksdxWGF6IU2HCN-SJAPCfKUID8myGlCyT9063WXzjgN0QEKSWxXyvON671NJ56ifgDAIomN |
| CitedBy_id | crossref_primary_10_1063_5_0267682 crossref_primary_10_1002_mma_10050 crossref_primary_10_1016_j_jde_2024_12_038 crossref_primary_10_1515_jiip_2024_0011 |
| Cites_doi | 10.1007/BF02674332 10.1186/1687-2770-2013-180 10.1134/S0001434618070258 10.1088/0266-5611/26/1/015009 10.1088/0266-5611/20/5/006 10.1080/10652460802564837 10.1016/j.jmaa.2003.11.025 10.1088/0266-5611/19/3/312 10.1002/mma.8819 10.1007/s00020-013-2035-7 10.1093/qmath/haad004 10.1134/S0001434618010078 10.1080/17415970802538550 10.1007/s10688-010-0038-6 10.3390/math9202617 10.5556/j.tkjm.52.2021.3700 10.1134/S0001434616050163 10.1088/1361-6420/aba416 10.1007/s00025-012-0258-6 10.1007/978-3-030-47849-0 10.1007/s10231-019-00934-w 10.1007/s00025-007-0276-y 10.1090/S0077-1554-2014-00234-X 10.1515/jiip-2020-0058 10.1088/0266-5611/28/8/085008 10.1090/S0025-5718-1992-1106979-0 10.1016/j.cnsns.2020.105298 10.1088/0266-5611/26/5/055003 10.1016/S0304-0208(04)80159-2 10.1017/S030821050002521X 10.1090/proc/15155 10.1017/S0308210500012312 10.1016/j.jmaa.2007.02.012 10.3390/math11051138 10.1090/pspum/077/2459883 10.1007/s00025-023-01850-5 10.1007/978-3-0348-8247-7_8 10.1007/s00025-022-01819-w 10.1017/S0013091501000773 10.1002/mma.3380 10.1063/1.5048692 10.1016/S0377-0427(02)00579-4 10.1134/S0081543808010161 10.1007/s13324-021-00581-6 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s13324-023-00845-3 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1664-235X |
| ExternalDocumentID | 10_1007_s13324_023_00845_3 |
| GrantInformation_xml | – fundername: Russian Science Foundation grantid: 21-71-10001; 21-71-10001 funderid: http://dx.doi.org/10.13039/501100006769 |
| GroupedDBID | -EM 0R~ 0VY 203 2VQ 30V 4.4 406 408 409 875 96X AAAVM AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH AAZMS ABAKF ABBXA ABDZT ABECU ABFTV ABJNI ABJOX ABKCH ABMQK ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABXPI ACAOD ACDTI ACGFS ACHSB ACIWK ACKNC ACMLO ACOKC ACPIV ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEVLU AEXYK AFBBN AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKLTO ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ANMIH AUKKA AXYYD AYJHY BAPOH BGNMA CSCUP DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FERAY FIGPU FINBP FNLPD FRRFC FSGXE FYJPI GGCAI GGRSB GJIRD GQ6 GQ8 HF~ HMJXF HQYDN HRMNR HZ~ I0C IKXTQ IWAJR IXD IZIGR J-C J9A JBSCW JCJTX JZLTJ KOV LLZTM M4Y NPVJJ NQJWS NU0 O9- O93 O9J PT4 R9I RLLFE ROL RSV S1Z S27 SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE T13 TSG TSV U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 ZMTXR ~A9 AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC AEZWR AFDZB AFHIU AFOHR AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION |
| ID | FETCH-LOGICAL-c291t-a3ba18721f11536d0115b71ece1f5e9d3be9dc656f5c091f8343027b6260fdec3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001187009900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1664-2368 |
| IngestDate | Tue Nov 18 20:47:32 EST 2025 Sat Nov 29 06:22:59 EST 2025 Fri Feb 21 02:42:19 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | 34L40 Constructive algorithm Inverse spectral problems 34B24 34A55 Polynomials in the boundary conditions Sturm–Liouville operator Uniqueness theorem 34B09 Singular potential 34B07 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c291t-a3ba18721f11536d0115b71ece1f5e9d3be9dc656f5c091f8343027b6260fdec3 |
| ParticipantIDs | crossref_citationtrail_10_1007_s13324_023_00845_3 crossref_primary_10_1007_s13324_023_00845_3 springer_journals_10_1007_s13324_023_00845_3 |
| PublicationCentury | 2000 |
| PublicationDate | 20231000 |
| PublicationDateYYYYMMDD | 2023-10-01 |
| PublicationDate_xml | – month: 10 year: 2023 text: 20231000 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham |
| PublicationTitle | Analysis and mathematical physics |
| PublicationTitleAbbrev | Anal.Math.Phys |
| PublicationYear | 2023 |
| Publisher | Springer International Publishing |
| Publisher_xml | – name: Springer International Publishing |
| References | ButerinSAOn inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite intervalJ. Math. Anal. Appl.2007335173974923403521132.34010 FreilingGYurkoVDetermination of singular differential pencils from the Weyl functionAdv. Dyn. Syst. Appl.2012721711933009618 HrynivROMykytyukYVHalf-inverse spectral problems for Sturm–Liouville operators with singular potentialsInverse probl.20042051423144421091271074.34007 FreilingGIgnatievMYYurkoVAAn inverse spectral problem for Sturm–Liouville operators with singular potentials on star-type graphProc. Symp. Pure Math.20087739740824598831159.34007 IgnatievMYurkoVNumerical methods for solving inverse Sturm–Liouville problemsResults Math.2008521–2637424304131147.65062 Chugunova, M.V.: Inverse spectral problem for the Sturm–Liouville operator with eigenvalue parameter dependent boundary conditions. In: Operator Theory: Advances and Applications, vol. 123, Birkhauser, Basel, pp. 187–194 (2001) BondarenkoNPSolving an inverse problem for the Sturm–Liouville operator with a singular potential by Yurko’s methodTamkang J. Math.202152112515442095691476.34060 Marchenko, V.A.: Sturm–Liouville Operators and Their Applications. Naukova Dumka, Kiev (1977) (Russian); English transl., Birkhauser (1986) BindingPABrownePJWatsonBASturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. IProc. Edinb. Math. Soc. (2)200245363164519337441019.34027 YurkoVAMethod of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series2002UtrechtVNU Science1098.34008 SavchukAMShkalikovAASturm–Liouville operators with distribution potentialsTransl. Moscow Math. Soc.20036414319220301891066.34085 ButerinSAShiehC-TYurkoVAInverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditionsBound. Value Probl.2013201318031030011297.34020 Ping, Y.W., Shieh C.-T., Tang, Y.: The partial inverse spectral problems for a differential operator. Results Math. 78, Article number: 44 (2023) HrynivRPronskaNInverse spectral problems for energy-dependent Sturm–Liouville equationsInverse Probl.201228085008 (21 pp)29565671256.34011 SavchukAMShkalikovAAInverse problems for Sturm–Liouville operators with potentials in Sobolev spaces: uniform stabilityFunct. Anal. Appl.201044427028527685631271.34017 KravchenkoVVDirect and Inverse Sturm–Liouville Problems2020ChamBirkhäuser07214198 Wang, Y.P., Keskin, B., Shieh, C.-T.: A partial inverse problem for non-self-adjoint Sturm–Liouville operators with a constant delay. J. Inverse Ill-Posed Probl. (2023). https://doi.org/10.1515/jiip-2020-0058 WangYPUniqueness theorems for Sturm–Liouville operators with boundary conditions polynomially dependent on the eigenparameter from spectral dataResults Math.2013631131114430573591279.34027 MirzoevKAShkalikovAADifferential operators of even order with distribution coefficientsMath. Notes201699577978435074441394.47046 KonechnajaNNMirzoevKAShkalikovAAOn the asymptotic behavior of solutions to two-term differential equations with singular coefficientsMath. Notes2018104224425238334981403.34060 BindingPABrownePJWatsonBAEquivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameterJ. Math. Anal. Appl.200429124626120340711046.34021 SavchukAMShkalikovAASturm–Liouville operators with singular potentialsMath. Notes199966674175317566020968.34072 Bondarenko, N.P.: Inverse problem solution and spectral data characterization for the matrix Sturm–Liouville operator with singular potential. Anal. Math. Phys. 11, Article number: 145 (2021) Buterin, S.: Functional-differential operators on geometrical graphs with global delay and inverse spectral problems. Results Math. 78(3), Article number: 79 (2023) BondarenkoNButerinSNumerical solution and stability of the inverse spectral problem for a convolution integro-differential operatorCommun. Nonlinear Sci. Numer. Simul.20208940979011452.65416 PronskaNReconstruction of energy-dependent Sturm-D-Liouville equations from two spectraIntegr. Equ. Oper. Theory20137640341930653011280.34016 BindingPABrownePJWatsonBASturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. IIJ. Comput. Appl. Math.2002148114716819461931019.34028 MykytyukYVTrushNSInverse spectral problems for Sturm–Liouville operators with matrix-valued potentialsInverse Probl.200926125753541195.34022 GuliyevNJEssentially isospectral transformations and their applicationsAnnali di Matematica Pura ed Applicata202019941621164841175111448.34064 GuliyevNJSchrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameterJ. Math. Phys.20196039591381416.81056 HrynivROMykytyukYVInverse spectral problems for Sturm–Liouville operators with singular potentialsInverse Probl.200319366568419848831034.34011 Bondarenko, N.P., Chitorkin, E.E.: Inverse Sturm–Liouville problem with spectral parameter in the boundary conditions. Mathematics 11(5), Article ID 1138 (2023) MirzoevKASturm–Liouville operatorsTrans. Moscow Math. Soc.20147528129933086131321.34042 HrynivROMankoSSInverse scattering on the half-line for energy-dependent Schrödinger equationsInverse Probl.20203691458.34142 KuznetsovaMAOn recovering quadratic pencils with singular coefficients and entire functions in the boundary conditionsMath. Methods Appl. Sci.2023465508650984564041 FreilingGYurkoVInverse Sturm–Liouville Problems and Their Applications2001HuntingtonNova Science Publishers1037.34005 FultonCTTwo-point boundary value problems with eigenvalue parameter contained in the boundary conditionsProc. R. Soc. Edinb. Sect. A.1977773–42933085931720376.34008 EckhardtJGesztesyFNicholsRSakhnovichATeschlGInverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentialsDiffer. Integr. Equ.2015285/65055221340.34053 YangC-FXuX-CAmbarzumyan-type theorem with polynomially dependent eigenparameterMath. Methods Appl. Sci.2015384411441534343671338.34047 Levitan, B.M.: Inverse Sturm–Liouville Problems. Nauka, Moscow (1984) (Russian); English transl., VNU Sci. Press, Utrecht (1987) Bondarenko N.P., Gaidel A.V.: Solvability and stability of the inverse problem for the quadratic differential pencil. Mathematics 9(20), Article ID 2617 (2021) PöschelJTrubowitzEInverse Spectral Theory1987New YorkAcademic Press0623.34001 HrynivROMykytyukYVInverse spectral problems for Sturm–Liouville operators with singular potentials. II. Reconstruction by two spectraNorth-Holland Math. Stud.20041979711420988741095.34008 AlbeverioSGesztesyFHoegh-KrohnRHoldenHSolvable Models in Quantum Mechanics20052ProvidnceAMS Chelsea Publishing1078.81003 FultonCTSingular eigenvalue problems with eigenvalue parameter contained in the boundary conditionsProc. R. Soc. Edinb. Sect. A.1980871–21346004460458.34013 GuliyevNJInverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coinQ. J. Math.2023464224210.1093/qmath/haad004 FreilingGYurkoVInverse problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameterInverse Probl.201026526471451207.47039 DjakovPMityaginBNSpectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentialsIntegr. Transforms Spec. Funct.2009203–42652731176.34108 YangYWeiGInverse scattering problems for Sturm–Liouville operators with spectral parameter dependent on boundary conditionsMath. Notes20181031–2596637402861398.34128 ChernozhukovaAFreilingGA uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditionsInverse Probl. Sci. Eng.200917677778525617141187.34016 GuliyevNJOn two-spectra inverse problemsProc. AMS.20201484491450241353131485.34083 RundellWSacksEReconstruction techniques for classical inverse Sturm–Liouville problemsMath. Comput.19925819716118311069790745.34015 SavchukAMShkalikovAAInverse problem for Sturm–Liouville operators with distribution potentials: reconstruction from two spectraRuss. J. Math. Phys.200512450751422013151396.34008 SavchukAMShkalikovAAOn the properties of maps connected with inverse Sturm–Liouville problemsProc. Steklov Inst. Math.200826021823724895151233.34010 CT Fulton (845_CR5) 1977; 77 NJ Guliyev (845_CR17) 2019; 60 AM Savchuk (845_CR25) 2003; 64 NP Bondarenko (845_CR37) 2021; 52 NN Konechnaja (845_CR33) 2018; 104 J Pöschel (845_CR3) 1987 PA Binding (845_CR8) 2002; 45 G Freiling (845_CR12) 2010; 26 RO Hryniv (845_CR26) 2003; 19 845_CR7 C-F Yang (845_CR15) 2015; 38 YV Mykytyuk (845_CR44) 2009; 26 A Chernozhukova (845_CR11) 2009; 17 N Pronska (845_CR40) 2013; 76 SA Buterin (845_CR48) 2013; 2013 KA Mirzoev (845_CR31) 2014; 75 845_CR42 Y Yang (845_CR16) 2018; 103 845_CR46 KA Mirzoev (845_CR32) 2016; 99 AM Savchuk (845_CR28) 2005; 12 W Rundell (845_CR50) 1992; 58 P Djakov (845_CR36) 2009; 20 cr-split#-845_CR2.1 cr-split#-845_CR2.2 RO Hryniv (845_CR34) 2004; 20 YP Wang (845_CR14) 2013; 63 VV Kravchenko (845_CR51) 2020 N Bondarenko (845_CR52) 2020; 89 CT Fulton (845_CR6) 1980; 87 J Eckhardt (845_CR45) 2015; 28 845_CR53 AM Savchuk (845_CR24) 1999; 66 G Freiling (845_CR35) 2008; 77 845_CR54 SA Buterin (845_CR47) 2007; 335 NJ Guliyev (845_CR19) 2020; 148 G Freiling (845_CR4) 2001 AM Savchuk (845_CR30) 2010; 44 PA Binding (845_CR10) 2004; 291 M Ignatiev (845_CR49) 2008; 52 R Hryniv (845_CR39) 2012; 28 NJ Guliyev (845_CR20) 2023 AM Savchuk (845_CR29) 2008; 260 845_CR22 S Albeverio (845_CR38) 2005 845_CR21 VA Yurko (845_CR23) 2002 RO Hryniv (845_CR41) 2020; 36 MA Kuznetsova (845_CR43) 2023; 46 cr-split#-845_CR1.1 cr-split#-845_CR1.2 PA Binding (845_CR9) 2002; 148 RO Hryniv (845_CR27) 2004; 197 G Freiling (845_CR13) 2012; 7 NJ Guliyev (845_CR18) 2020; 199 |
| References_xml | – reference: GuliyevNJOn two-spectra inverse problemsProc. AMS.20201484491450241353131485.34083 – reference: DjakovPMityaginBNSpectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentialsIntegr. Transforms Spec. Funct.2009203–42652731176.34108 – reference: GuliyevNJEssentially isospectral transformations and their applicationsAnnali di Matematica Pura ed Applicata202019941621164841175111448.34064 – reference: SavchukAMShkalikovAAOn the properties of maps connected with inverse Sturm–Liouville problemsProc. Steklov Inst. Math.200826021823724895151233.34010 – reference: SavchukAMShkalikovAAInverse problems for Sturm–Liouville operators with potentials in Sobolev spaces: uniform stabilityFunct. Anal. Appl.201044427028527685631271.34017 – reference: MykytyukYVTrushNSInverse spectral problems for Sturm–Liouville operators with matrix-valued potentialsInverse Probl.200926125753541195.34022 – reference: MirzoevKAShkalikovAADifferential operators of even order with distribution coefficientsMath. Notes201699577978435074441394.47046 – reference: Ping, Y.W., Shieh C.-T., Tang, Y.: The partial inverse spectral problems for a differential operator. Results Math. 78, Article number: 44 (2023) – reference: BondarenkoNPSolving an inverse problem for the Sturm–Liouville operator with a singular potential by Yurko’s methodTamkang J. Math.202152112515442095691476.34060 – reference: ChernozhukovaAFreilingGA uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditionsInverse Probl. Sci. Eng.200917677778525617141187.34016 – reference: Bondarenko, N.P., Chitorkin, E.E.: Inverse Sturm–Liouville problem with spectral parameter in the boundary conditions. Mathematics 11(5), Article ID 1138 (2023) – reference: AlbeverioSGesztesyFHoegh-KrohnRHoldenHSolvable Models in Quantum Mechanics20052ProvidnceAMS Chelsea Publishing1078.81003 – reference: SavchukAMShkalikovAASturm–Liouville operators with singular potentialsMath. Notes199966674175317566020968.34072 – reference: FultonCTTwo-point boundary value problems with eigenvalue parameter contained in the boundary conditionsProc. R. Soc. Edinb. Sect. A.1977773–42933085931720376.34008 – reference: SavchukAMShkalikovAAInverse problem for Sturm–Liouville operators with distribution potentials: reconstruction from two spectraRuss. J. Math. Phys.200512450751422013151396.34008 – reference: HrynivROMykytyukYVInverse spectral problems for Sturm–Liouville operators with singular potentials. II. Reconstruction by two spectraNorth-Holland Math. Stud.20041979711420988741095.34008 – reference: KuznetsovaMAOn recovering quadratic pencils with singular coefficients and entire functions in the boundary conditionsMath. Methods Appl. Sci.2023465508650984564041 – reference: SavchukAMShkalikovAASturm–Liouville operators with distribution potentialsTransl. Moscow Math. Soc.20036414319220301891066.34085 – reference: HrynivROMankoSSInverse scattering on the half-line for energy-dependent Schrödinger equationsInverse Probl.20203691458.34142 – reference: WangYPUniqueness theorems for Sturm–Liouville operators with boundary conditions polynomially dependent on the eigenparameter from spectral dataResults Math.2013631131114430573591279.34027 – reference: ButerinSAOn inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite intervalJ. Math. Anal. Appl.2007335173974923403521132.34010 – reference: YangYWeiGInverse scattering problems for Sturm–Liouville operators with spectral parameter dependent on boundary conditionsMath. Notes20181031–2596637402861398.34128 – reference: KonechnajaNNMirzoevKAShkalikovAAOn the asymptotic behavior of solutions to two-term differential equations with singular coefficientsMath. Notes2018104224425238334981403.34060 – reference: Chugunova, M.V.: Inverse spectral problem for the Sturm–Liouville operator with eigenvalue parameter dependent boundary conditions. In: Operator Theory: Advances and Applications, vol. 123, Birkhauser, Basel, pp. 187–194 (2001) – reference: Buterin, S.: Functional-differential operators on geometrical graphs with global delay and inverse spectral problems. Results Math. 78(3), Article number: 79 (2023) – reference: FreilingGYurkoVDetermination of singular differential pencils from the Weyl functionAdv. Dyn. Syst. Appl.2012721711933009618 – reference: RundellWSacksEReconstruction techniques for classical inverse Sturm–Liouville problemsMath. Comput.19925819716118311069790745.34015 – reference: HrynivROMykytyukYVInverse spectral problems for Sturm–Liouville operators with singular potentialsInverse Probl.200319366568419848831034.34011 – reference: FultonCTSingular eigenvalue problems with eigenvalue parameter contained in the boundary conditionsProc. R. Soc. Edinb. Sect. A.1980871–21346004460458.34013 – reference: IgnatievMYurkoVNumerical methods for solving inverse Sturm–Liouville problemsResults Math.2008521–2637424304131147.65062 – reference: BondarenkoNButerinSNumerical solution and stability of the inverse spectral problem for a convolution integro-differential operatorCommun. Nonlinear Sci. Numer. Simul.20208940979011452.65416 – reference: FreilingGYurkoVInverse problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameterInverse Probl.201026526471451207.47039 – reference: ButerinSAShiehC-TYurkoVAInverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditionsBound. Value Probl.2013201318031030011297.34020 – reference: Levitan, B.M.: Inverse Sturm–Liouville Problems. Nauka, Moscow (1984) (Russian); English transl., VNU Sci. Press, Utrecht (1987) – reference: GuliyevNJInverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coinQ. J. Math.2023464224210.1093/qmath/haad004 – reference: BindingPABrownePJWatsonBASturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. IProc. Edinb. Math. Soc. (2)200245363164519337441019.34027 – reference: YurkoVAMethod of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series2002UtrechtVNU Science1098.34008 – reference: GuliyevNJSchrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameterJ. Math. Phys.20196039591381416.81056 – reference: PronskaNReconstruction of energy-dependent Sturm-D-Liouville equations from two spectraIntegr. Equ. Oper. Theory20137640341930653011280.34016 – reference: Bondarenko N.P., Gaidel A.V.: Solvability and stability of the inverse problem for the quadratic differential pencil. Mathematics 9(20), Article ID 2617 (2021) – reference: MirzoevKASturm–Liouville operatorsTrans. Moscow Math. Soc.20147528129933086131321.34042 – reference: EckhardtJGesztesyFNicholsRSakhnovichATeschlGInverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentialsDiffer. Integr. Equ.2015285/65055221340.34053 – reference: BindingPABrownePJWatsonBASturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. IIJ. Comput. Appl. Math.2002148114716819461931019.34028 – reference: FreilingGIgnatievMYYurkoVAAn inverse spectral problem for Sturm–Liouville operators with singular potentials on star-type graphProc. Symp. Pure Math.20087739740824598831159.34007 – reference: HrynivRPronskaNInverse spectral problems for energy-dependent Sturm–Liouville equationsInverse Probl.201228085008 (21 pp)29565671256.34011 – reference: Marchenko, V.A.: Sturm–Liouville Operators and Their Applications. Naukova Dumka, Kiev (1977) (Russian); English transl., Birkhauser (1986) – reference: YangC-FXuX-CAmbarzumyan-type theorem with polynomially dependent eigenparameterMath. Methods Appl. Sci.2015384411441534343671338.34047 – reference: Wang, Y.P., Keskin, B., Shieh, C.-T.: A partial inverse problem for non-self-adjoint Sturm–Liouville operators with a constant delay. J. Inverse Ill-Posed Probl. (2023). https://doi.org/10.1515/jiip-2020-0058 – reference: HrynivROMykytyukYVHalf-inverse spectral problems for Sturm–Liouville operators with singular potentialsInverse probl.20042051423144421091271074.34007 – reference: FreilingGYurkoVInverse Sturm–Liouville Problems and Their Applications2001HuntingtonNova Science Publishers1037.34005 – reference: PöschelJTrubowitzEInverse Spectral Theory1987New YorkAcademic Press0623.34001 – reference: Bondarenko, N.P.: Inverse problem solution and spectral data characterization for the matrix Sturm–Liouville operator with singular potential. Anal. Math. Phys. 11, Article number: 145 (2021) – reference: KravchenkoVVDirect and Inverse Sturm–Liouville Problems2020ChamBirkhäuser07214198 – reference: BindingPABrownePJWatsonBAEquivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameterJ. Math. Anal. Appl.200429124626120340711046.34021 – volume: 66 start-page: 741 issue: 6 year: 1999 ident: 845_CR24 publication-title: Math. Notes doi: 10.1007/BF02674332 – volume: 2013 start-page: 180 year: 2013 ident: 845_CR48 publication-title: Bound. Value Probl. doi: 10.1186/1687-2770-2013-180 – volume: 104 start-page: 244 issue: 2 year: 2018 ident: 845_CR33 publication-title: Math. Notes doi: 10.1134/S0001434618070258 – volume: 26 issue: 1 year: 2009 ident: 845_CR44 publication-title: Inverse Probl. doi: 10.1088/0266-5611/26/1/015009 – volume: 20 start-page: 1423 issue: 5 year: 2004 ident: 845_CR34 publication-title: Inverse probl. doi: 10.1088/0266-5611/20/5/006 – volume: 20 start-page: 265 issue: 3–4 year: 2009 ident: 845_CR36 publication-title: Integr. Transforms Spec. Funct. doi: 10.1080/10652460802564837 – volume: 291 start-page: 246 year: 2004 ident: 845_CR10 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2003.11.025 – volume: 19 start-page: 665 issue: 3 year: 2003 ident: 845_CR26 publication-title: Inverse Probl. doi: 10.1088/0266-5611/19/3/312 – ident: #cr-split#-845_CR2.1 – volume-title: Solvable Models in Quantum Mechanics year: 2005 ident: 845_CR38 – volume: 46 start-page: 5086 issue: 5 year: 2023 ident: 845_CR43 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.8819 – ident: #cr-split#-845_CR1.2 – volume: 76 start-page: 403 year: 2013 ident: 845_CR40 publication-title: Integr. Equ. Oper. Theory doi: 10.1007/s00020-013-2035-7 – year: 2023 ident: 845_CR20 publication-title: Q. J. Math. doi: 10.1093/qmath/haad004 – volume: 103 start-page: 59 issue: 1–2 year: 2018 ident: 845_CR16 publication-title: Math. Notes doi: 10.1134/S0001434618010078 – volume: 17 start-page: 777 issue: 6 year: 2009 ident: 845_CR11 publication-title: Inverse Probl. Sci. Eng. doi: 10.1080/17415970802538550 – volume-title: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series year: 2002 ident: 845_CR23 – volume: 44 start-page: 270 issue: 4 year: 2010 ident: 845_CR30 publication-title: Funct. Anal. Appl. doi: 10.1007/s10688-010-0038-6 – ident: 845_CR42 doi: 10.3390/math9202617 – volume: 52 start-page: 125 issue: 1 year: 2021 ident: 845_CR37 publication-title: Tamkang J. Math. doi: 10.5556/j.tkjm.52.2021.3700 – volume: 99 start-page: 779 issue: 5 year: 2016 ident: 845_CR32 publication-title: Math. Notes doi: 10.1134/S0001434616050163 – volume-title: Inverse Sturm–Liouville Problems and Their Applications year: 2001 ident: 845_CR4 – volume: 36 issue: 9 year: 2020 ident: 845_CR41 publication-title: Inverse Probl. doi: 10.1088/1361-6420/aba416 – ident: #cr-split#-845_CR1.1 – volume: 63 start-page: 1131 year: 2013 ident: 845_CR14 publication-title: Results Math. doi: 10.1007/s00025-012-0258-6 – volume-title: Direct and Inverse Sturm–Liouville Problems year: 2020 ident: 845_CR51 doi: 10.1007/978-3-030-47849-0 – volume: 12 start-page: 507 issue: 4 year: 2005 ident: 845_CR28 publication-title: Russ. J. Math. Phys. – volume: 199 start-page: 1621 issue: 4 year: 2020 ident: 845_CR18 publication-title: Annali di Matematica Pura ed Applicata doi: 10.1007/s10231-019-00934-w – volume: 52 start-page: 63 issue: 1–2 year: 2008 ident: 845_CR49 publication-title: Results Math. doi: 10.1007/s00025-007-0276-y – volume: 28 start-page: 505 issue: 5/6 year: 2015 ident: 845_CR45 publication-title: Differ. Integr. Equ. – volume: 75 start-page: 281 year: 2014 ident: 845_CR31 publication-title: Trans. Moscow Math. Soc. doi: 10.1090/S0077-1554-2014-00234-X – ident: 845_CR54 doi: 10.1515/jiip-2020-0058 – volume: 28 start-page: 085008 (21 pp) year: 2012 ident: 845_CR39 publication-title: Inverse Probl. doi: 10.1088/0266-5611/28/8/085008 – volume: 58 start-page: 161 issue: 197 year: 1992 ident: 845_CR50 publication-title: Math. Comput. doi: 10.1090/S0025-5718-1992-1106979-0 – volume: 89 year: 2020 ident: 845_CR52 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2020.105298 – volume: 26 issue: 5 year: 2010 ident: 845_CR12 publication-title: Inverse Probl. doi: 10.1088/0266-5611/26/5/055003 – volume: 197 start-page: 97 year: 2004 ident: 845_CR27 publication-title: North-Holland Math. Stud. doi: 10.1016/S0304-0208(04)80159-2 – volume: 77 start-page: 293 issue: 3–4 year: 1977 ident: 845_CR5 publication-title: Proc. R. Soc. Edinb. Sect. A. doi: 10.1017/S030821050002521X – volume: 148 start-page: 4491 year: 2020 ident: 845_CR19 publication-title: Proc. AMS. doi: 10.1090/proc/15155 – volume: 87 start-page: 1 issue: 1–2 year: 1980 ident: 845_CR6 publication-title: Proc. R. Soc. Edinb. Sect. A. doi: 10.1017/S0308210500012312 – volume: 64 start-page: 143 year: 2003 ident: 845_CR25 publication-title: Transl. Moscow Math. Soc. – volume: 335 start-page: 739 issue: 1 year: 2007 ident: 845_CR47 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.02.012 – ident: 845_CR21 doi: 10.3390/math11051138 – volume: 7 start-page: 171 issue: 2 year: 2012 ident: 845_CR13 publication-title: Adv. Dyn. Syst. Appl. – volume: 77 start-page: 397 year: 2008 ident: 845_CR35 publication-title: Proc. Symp. Pure Math. doi: 10.1090/pspum/077/2459883 – ident: 845_CR53 doi: 10.1007/s00025-023-01850-5 – ident: 845_CR7 doi: 10.1007/978-3-0348-8247-7_8 – ident: 845_CR22 doi: 10.1007/s00025-022-01819-w – volume: 45 start-page: 631 issue: 3 year: 2002 ident: 845_CR8 publication-title: Proc. Edinb. Math. Soc. (2) doi: 10.1017/S0013091501000773 – volume: 38 start-page: 4411 year: 2015 ident: 845_CR15 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3380 – volume: 60 year: 2019 ident: 845_CR17 publication-title: J. Math. Phys. doi: 10.1063/1.5048692 – ident: #cr-split#-845_CR2.2 – volume: 148 start-page: 147 issue: 1 year: 2002 ident: 845_CR9 publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00579-4 – volume: 260 start-page: 218 year: 2008 ident: 845_CR29 publication-title: Proc. Steklov Inst. Math. doi: 10.1134/S0081543808010161 – ident: 845_CR46 doi: 10.1007/s13324-021-00581-6 – volume-title: Inverse Spectral Theory year: 1987 ident: 845_CR3 |
| SSID | ssj0001456467 |
| Score | 2.3086615 |
| Snippet | In this paper, we for the first time get constructive solution for the inverse Sturm–Liouville problem with complex-valued singular potential and with... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| SubjectTerms | Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics |
| Title | Solving the inverse Sturm–Liouville problem with singular potential and with polynomials in the boundary conditions |
| URI | https://link.springer.com/article/10.1007/s13324-023-00845-3 |
| Volume | 13 |
| WOSCitedRecordID | wos001187009900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLink customDbUrl: eissn: 1664-235X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001456467 issn: 1664-2368 databaseCode: RSV dateStart: 20110301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEF60etCD1apYX-zBmy4k2TyPIhYPtYjV0lvIbnahUJPStIXe_A_-Q3-JM8m2pSAFveSQTDbLPvLNzH4zQ8hNpDUAkZMyD3ehCwYAE5EvWahUYgdcWaJk-fbaQacT9vvRiwkKKxZs98WRZPmnXgW7cQB_BhjDMAm8x_g22QG4C5DI99rtrTwrmCGlLB1r-77LHO6HJlrm92bWEWn9OLREmVb9f_07JAdGq6T31TI4Ilsqa5C60TCp2b9Fg-w_L7O0Fsdk2s2H6E-gcI8OMiRoKNoFDPr4_vxqD_LpDAMFqak5Q9FlS9G1gMxVOsonSDSCryZZWj0b5cM5RjnDiobmylZFWbVpPKdgdqcVO-yEvLce3x6emCnDwKQT2ROWcJHYIViKGrRH7qeoRIrAVlLZ2lNRygVcJOiF2pOgfeiQu3gYKtBU0qmS_JTUsjxTZ4Q6qZSWpx0hUtdVAIvas1VgKR44ypWW3yT2YipiaXKUY6mMYbzKroyjHMMox-Uox7xJbpfvjKoMHRul7xazF5vdWmwQP_-b-AXZw3L0FdnvktQm46m6IrtyNhkU4-tymf4AtoLjLQ |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB60CurBt_h2D950ocnmeRSxKNYiVIu30N3sQqEmpWkLvfkf_If-EmeSrUUQQS85JJtN2Ozm-2b2mxmA89gYBCI35T6tQg8NAC7jQPFI664TCl2Xpcq30wxbrejlJX60QWHFTO0-25Is_9TzYDeB4M8RYzglgfe5WIQlz0WGTzZ6uzP3rFCGlLJ0rBMEHndFENlomZ-7-Y5I37dDS5RpbPzv_TZh3bJKdlVNgy1Y0Nk2bFiGyez6LbZh7eErS2uxA-N23id_AsNzrJeRQEOzNmLQ68fbe7OXjycUKMhszRlGLltGrgVSrrJBPiKhET61m6XVtUHen1KUM85o7K7sVZZVm4ZThmZ3WqnDduG5cfN0fcttGQau3NgZ8a6QXSdCS9EgexRBSiRSho5W2jG-jlMh8aCQFxpfIfswkfBoM1SSqWRSrcQe1LI80_vA3FSpum9cKVPP0wiLxnd0WNcidLWn6sEBOLNPkSibo5xKZfSTeXZlGuUERzkpRzkRB3Dxdc-gytDxa-vL2ddL7Gotfml--LfmZ7By-_TQTJp3rfsjWKXS9JXw7xhqo-FYn8Cymox6xfC0nLKfZWLmEQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60iujBt_h2D950scnmeRS1KNYiVMVb6L6gUJPSF3jzP_gP_SXOJKm1IIJ4ySHZLPuYZb6Z_WYG4Di2FhWRq7lPp9BDA4DLOFA8MqblhMJUZc7yfaqHjUb0_Bzff4viz9nu4yvJIqaBsjSlg7OutmeTwDeBQICjvuGUEN7nYhbmPKLLkb3efJp4WShbSl5G1gkCj7siiMrImZ-7mdZO01ejucaprfx_rKuwXKJNdl6IxxrMmHQdVkrkycpz3V-Hpbuv7K39DRg2sw75GRi-Y-2UiBuGNVE3vXy8vdfb2XBEAYSsrEXDyJXLyOVAjFbWzWhsKNWsleriWzfrvFL0M0o6dpf3KvNqTr1XhnPRBWtsEx5rVw8X17wsz8CVGzsD3hKy5URoQVpElSLQBC5l6BhlHOubWAuJD4V40foKUYmNhEeXpJJMKKuNEltQSbPUbANztVJV37pSas8zqC6t75iwakToGk9Vgx1wxtuSqDJ3OZXQ6CSTrMu0ygmucpKvciJ24OTrn26RuePX1qfjnUzKU9z_pfnu35ofwcL9ZS2p3zRu92CRKtYXfMB9qAx6Q3MA82o0aPd7h7n0fgIZOO7s |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Solving+the+inverse+Sturm%E2%80%93Liouville+problem+with+singular+potential+and+with+polynomials+in+the+boundary+conditions&rft.jtitle=Analysis+and+mathematical+physics&rft.au=Chitorkin%2C+Egor+E.&rft.au=Bondarenko%2C+Natalia+P.&rft.date=2023-10-01&rft.issn=1664-2368&rft.eissn=1664-235X&rft.volume=13&rft.issue=5&rft_id=info:doi/10.1007%2Fs13324-023-00845-3&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s13324_023_00845_3 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1664-2368&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1664-2368&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1664-2368&client=summon |