Orbits of the backward shifts with limit points
We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓ...
Uloženo v:
| Vydáno v: | Journal of mathematical analysis and applications Ročník 537; číslo 2; s. 128293 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
15.09.2024
|
| Témata: | |
| ISSN: | 0022-247X |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓp(N,ω) such that its orbit under the unilateral backward shift B on ℓp(N,ω) has a non-zero weak limit point, then B is hypercyclic. Similar results for translation semigroups on weighted Lebesgue spaces are obtained. |
|---|---|
| AbstractList | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓp(N,ω) such that its orbit under the unilateral backward shift B on ℓp(N,ω) has a non-zero weak limit point, then B is hypercyclic. Similar results for translation semigroups on weighted Lebesgue spaces are obtained. |
| ArticleNumber | 128293 |
| Author | Abakumov, Evgeny Abbar, Arafat |
| Author_xml | – sequence: 1 givenname: Evgeny surname: Abakumov fullname: Abakumov, Evgeny email: evgueni.abakoumov@univ-eiffel.fr – sequence: 2 givenname: Arafat orcidid: 0000-0002-8788-1001 surname: Abbar fullname: Abbar, Arafat email: abbar.arafat@gmail.com |
| BookMark | eNp9z79qwzAQx3ENKTRJ-wKd_AJ2TmdbtqFLCf0HgSwtdBOSLONzHTtIoqFvXwd3ypDp4OD7g8-KLYZxsIw9cEg4cLHpku6gVIKAWcKxxCpdsCUAYoxZ8XXLVt53AJznBV-yzd5pCj4amyi0NtLKfJ-UqyPfUjO9TxTaqKcDheg40hD8HbtpVO_t_f9ds8-X54_tW7zbv75vn3axSQFCrGpVYaOFBdQ6zSxoA5WqoBIZF2ldGo6i4FDmGWqjCyFqpVHkTZ5pLEqdpmuG865xo_fONvLo6KDcr-Qgz0zZyTNTnplyZk5ReREZCirQOASnqL-ePs6pnVA_ZJ30huxgbE3OmiDrka7lf0JecP4 |
| CitedBy_id | crossref_primary_10_4153_S0008414X24000981 |
| Cites_doi | 10.1090/S0002-9947-1995-1249890-6 10.4064/sm-135-1-55-74 10.1090/S0273-0979-99-00788-0 10.4064/sm-32-1-17-22 10.1016/j.jmaa.2017.11.046 10.1007/s11785-019-00941-y 10.1016/j.jmaa.2010.08.033 10.1307/mmj/1029005229 10.1142/S0218127418500761 10.1007/s11785-013-0348-9 10.1090/S0002-9939-03-06960-0 10.1016/j.jmaa.2020.124709 10.1017/S0143385797084976 10.1007/s00020-013-2100-2 10.1016/j.jfa.2006.12.008 10.7146/math.scand.a-15207 10.1016/j.jfa.2016.03.005 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier Inc. |
| Copyright_xml | – notice: 2024 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.jmaa.2024.128293 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| ExternalDocumentID | 10_1016_j_jmaa_2024_128293 S0022247X24002154 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 4.4 457 4G. 5GY 71M 85S 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AAOAW AAQFI AASFE AAXKI AAXUO ABAOU ABJNI ABMAC ABVKL ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AFJKZ AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DM4 EBS EFBJH EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM LG5 M25 M41 MCRUF MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW T5K TN5 TWZ UPT WH7 XPP YQT ZMT ZU3 ~G- 1~5 29L 5VS 6TJ 7-5 9DU AALRI AAQXK AATTM AAYWO AAYXX ABDPE ABEFU ABFNM ABUFD ABWVN ABXDB ACLOT ACRPL ACVFH ADCNI ADFGL ADIYS ADMUD ADNMO ADVLN ADXHL AEIPS AETEA AEUPX AEXQZ AFFNX AFPUW AGHFR AGQPQ AI. AIGII AIIUN AKBMS AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CAG CITATION COF EFKBS EFLBG EJD FGOYB G-2 HZ~ H~9 MVM OHT R2- SSZ VH1 VOH WUQ XOL YYP ZCG ~HD |
| ID | FETCH-LOGICAL-c300t-ada92fb6e02bb34e0bc09a90964163d8c1267108542bcb766dab265f54b278b33 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001218979600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0022-247X |
| IngestDate | Tue Nov 18 20:54:30 EST 2025 Sat Nov 29 03:27:13 EST 2025 Tue Dec 03 03:44:48 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Backward shift Recurrence Supercyclicity Hypercyclicity Translation semigroup Orbital limit points |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c300t-ada92fb6e02bb34e0bc09a90964163d8c1267108542bcb766dab265f54b278b33 |
| ORCID | 0000-0002-8788-1001 |
| ParticipantIDs | crossref_primary_10_1016_j_jmaa_2024_128293 crossref_citationtrail_10_1016_j_jmaa_2024_128293 elsevier_sciencedirect_doi_10_1016_j_jmaa_2024_128293 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-09-15 |
| PublicationDateYYYYMMDD | 2024-09-15 |
| PublicationDate_xml | – month: 09 year: 2024 text: 2024-09-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of mathematical analysis and applications |
| PublicationYear | 2024 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Charpentier, Ernst, Menet (br0080) 2016; 270 Grosse-Erdmann, Peris (br0170) 2011 Abbar (br0040) 2020 He, Huang, Yin (br0180) 2018; 28 Abbar (br0020) 2019; 13 Costakis, Manoussos, Parissis (br0100) 2014; 8 Rolewicz (br0200) 1969; 32 Desch, Schappacher, Webb (br0140) 1997; 17 Salas (br0220) 1999; 135 Yin, Wei (br0240) 2018; 460 Salas (br0210) 1995; 347 Bonilla, Grosse-Erdmann (br0070) 2020 Abbar (br0030) 2019; 129 Chan, Seceleanu (br0130) 2014; 78 Matsui, Yamada, Takeo (br0190) 2003; 131 Abakumov (br0010) 1995; 42 Chan, Seceleanu (br0120) 2012; 67 Conejero, Müller, Peris (br0090) 2007; 244 Costakis, Parissis (br0110) 2012; 110 Feldman (br0150) 2003; 50 Bayart, Matheron (br0060) 2009; vol. 179 Abbar, Kuznetsova (br0050) 2021; 495 Grosse-Erdmann (br0160) 1999; 36 Shkarin (br0230) 2011; 382 Chan (10.1016/j.jmaa.2024.128293_br0120) 2012; 67 Abbar (10.1016/j.jmaa.2024.128293_br0040) 2020 Rolewicz (10.1016/j.jmaa.2024.128293_br0200) 1969; 32 Salas (10.1016/j.jmaa.2024.128293_br0220) 1999; 135 Shkarin (10.1016/j.jmaa.2024.128293_br0230) 2011; 382 Desch (10.1016/j.jmaa.2024.128293_br0140) 1997; 17 Feldman (10.1016/j.jmaa.2024.128293_br0150) 2003; 50 Grosse-Erdmann (10.1016/j.jmaa.2024.128293_br0160) 1999; 36 Abbar (10.1016/j.jmaa.2024.128293_br0020) 2019; 13 Abbar (10.1016/j.jmaa.2024.128293_br0050) 2021; 495 Matsui (10.1016/j.jmaa.2024.128293_br0190) 2003; 131 Conejero (10.1016/j.jmaa.2024.128293_br0090) 2007; 244 Costakis (10.1016/j.jmaa.2024.128293_br0100) 2014; 8 Abbar (10.1016/j.jmaa.2024.128293_br0030) 2019; 129 He (10.1016/j.jmaa.2024.128293_br0180) 2018; 28 Yin (10.1016/j.jmaa.2024.128293_br0240) 2018; 460 Salas (10.1016/j.jmaa.2024.128293_br0210) 1995; 347 Grosse-Erdmann (10.1016/j.jmaa.2024.128293_br0170) 2011 Bonilla (10.1016/j.jmaa.2024.128293_br0070) Abakumov (10.1016/j.jmaa.2024.128293_br0010) 1995; 42 Charpentier (10.1016/j.jmaa.2024.128293_br0080) 2016; 270 Costakis (10.1016/j.jmaa.2024.128293_br0110) 2012; 110 Chan (10.1016/j.jmaa.2024.128293_br0130) 2014; 78 Bayart (10.1016/j.jmaa.2024.128293_br0060) 2009; vol. 179 |
| References_xml | – volume: 13 start-page: 3923 year: 2019 end-page: 3942 ident: br0020 article-title: Γ-supercyclicity for strongly continuous semigroups publication-title: Complex Anal. Oper. Theory – year: 2020 ident: br0040 article-title: Dynamique linéaire: ensembles hypercycliques, semigroupes d'opérateurs, translations sur les groupes – year: 2011 ident: br0170 article-title: Linear Chaos – volume: 131 start-page: 3535 year: 2003 end-page: 3546 ident: br0190 article-title: Supercyclic and chaotic translation semigroups publication-title: Proc. Am. Math. Soc. – volume: 244 start-page: 342 year: 2007 end-page: 348 ident: br0090 article-title: Hypercyclic behaviour of operators in a hypercyclic publication-title: J. Funct. Anal. – volume: 28 year: 2018 ident: br0180 article-title: -class weighted backward shifts publication-title: Int. J. Bifurc. Chaos – volume: 135 start-page: 55 year: 1999 end-page: 74 ident: br0220 article-title: Supercyclicity and weighted shifts publication-title: Stud. Math. – volume: 17 start-page: 793 year: 1997 end-page: 819 ident: br0140 article-title: Hypercyclic and chaotic semigroups of linear operators publication-title: Ergod. Theory Dyn. Syst. – volume: 50 start-page: 107 year: 2003 end-page: 117 ident: br0150 article-title: Countably hypercyclic operators publication-title: J. Oper. Theory – volume: 8 start-page: 1601 year: 2014 end-page: 1643 ident: br0100 article-title: Recurrent linear operators publication-title: Complex Anal. Oper. Theory – volume: 42 start-page: 277 year: 1995 end-page: 299 ident: br0010 article-title: Cyclicity and approximation by lacunary power series publication-title: Mich. Math. J. – volume: 270 start-page: 4443 year: 2016 end-page: 4465 ident: br0080 article-title: Γ-supercyclicity publication-title: J. Funct. Anal. – volume: 78 start-page: 225 year: 2014 end-page: 232 ident: br0130 article-title: Cyclicity of vectors with orbital limit points for backward shifts publication-title: Integral Equ. Oper. Theory – volume: 382 start-page: 516 year: 2011 end-page: 522 ident: br0230 article-title: On supercyclicity of operators from a supercyclic semigroup publication-title: J. Math. Anal. Appl. – volume: 110 start-page: 251 year: 2012 end-page: 272 ident: br0110 article-title: Szemerédi's theorem, frequent hypercyclicity and multiple recurrence publication-title: Math. Scand. – volume: 67 start-page: 257 year: 2012 end-page: 277 ident: br0120 article-title: Hypercyclicity of shifts as a zero-one law of orbital limit points publication-title: J. Oper. Theory – volume: 32 start-page: 17 year: 1969 end-page: 22 ident: br0200 article-title: On orbits of elements publication-title: Stud. Math. – volume: 347 start-page: 993 year: 1995 end-page: 1004 ident: br0210 article-title: Hypercyclic weighted shifts publication-title: Trans. Am. Math. Soc. – volume: 460 start-page: 203 year: 2018 end-page: 215 ident: br0240 article-title: Recurrence and topological entropy of translation operators publication-title: J. Math. Anal. Appl. – volume: 36 start-page: 345 year: 1999 end-page: 381 ident: br0160 article-title: Universal families and hypercyclic operators publication-title: Bull. Am. Math. Soc. – volume: 495 year: 2021 ident: br0050 article-title: Γ-supercyclicity of families of translates in weighted publication-title: J. Math. Anal. Appl. – year: 2020 ident: br0070 article-title: Zero-one law of orbital limit points for weighted shifts – volume: 129 start-page: 73 year: 2019 end-page: 79 ident: br0030 article-title: Γ-supercyclicity for bilateral shift operators and translation semigroups publication-title: Bul. L.N. Gumilyov ENU. Math. Comput. Sci. Mech. Ser. – volume: vol. 179 year: 2009 ident: br0060 article-title: Dynamics of Linear Operators publication-title: Cambridge Tracts in Mathematics – year: 2011 ident: 10.1016/j.jmaa.2024.128293_br0170 – volume: 129 start-page: 73 issue: 4 year: 2019 ident: 10.1016/j.jmaa.2024.128293_br0030 article-title: Γ-supercyclicity for bilateral shift operators and translation semigroups publication-title: Bul. L.N. Gumilyov ENU. Math. Comput. Sci. Mech. Ser. – year: 2020 ident: 10.1016/j.jmaa.2024.128293_br0040 – volume: 347 start-page: 993 issue: 3 year: 1995 ident: 10.1016/j.jmaa.2024.128293_br0210 article-title: Hypercyclic weighted shifts publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1995-1249890-6 – volume: 135 start-page: 55 issue: 1 year: 1999 ident: 10.1016/j.jmaa.2024.128293_br0220 article-title: Supercyclicity and weighted shifts publication-title: Stud. Math. doi: 10.4064/sm-135-1-55-74 – volume: 36 start-page: 345 issue: 3 year: 1999 ident: 10.1016/j.jmaa.2024.128293_br0160 article-title: Universal families and hypercyclic operators publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-99-00788-0 – volume: 32 start-page: 17 issue: 1 year: 1969 ident: 10.1016/j.jmaa.2024.128293_br0200 article-title: On orbits of elements publication-title: Stud. Math. doi: 10.4064/sm-32-1-17-22 – volume: 460 start-page: 203 issue: 1 year: 2018 ident: 10.1016/j.jmaa.2024.128293_br0240 article-title: Recurrence and topological entropy of translation operators publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.11.046 – volume: 13 start-page: 3923 issue: 8 year: 2019 ident: 10.1016/j.jmaa.2024.128293_br0020 article-title: Γ-supercyclicity for strongly continuous semigroups publication-title: Complex Anal. Oper. Theory doi: 10.1007/s11785-019-00941-y – volume: 382 start-page: 516 issue: 2 year: 2011 ident: 10.1016/j.jmaa.2024.128293_br0230 article-title: On supercyclicity of operators from a supercyclic semigroup publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2010.08.033 – volume: 42 start-page: 277 issue: 2 year: 1995 ident: 10.1016/j.jmaa.2024.128293_br0010 article-title: Cyclicity and approximation by lacunary power series publication-title: Mich. Math. J. doi: 10.1307/mmj/1029005229 – ident: 10.1016/j.jmaa.2024.128293_br0070 – volume: 28 issue: 06 year: 2018 ident: 10.1016/j.jmaa.2024.128293_br0180 article-title: JF-class weighted backward shifts publication-title: Int. J. Bifurc. Chaos doi: 10.1142/S0218127418500761 – volume: 8 start-page: 1601 issue: 8 year: 2014 ident: 10.1016/j.jmaa.2024.128293_br0100 article-title: Recurrent linear operators publication-title: Complex Anal. Oper. Theory doi: 10.1007/s11785-013-0348-9 – volume: 131 start-page: 3535 issue: 11 year: 2003 ident: 10.1016/j.jmaa.2024.128293_br0190 article-title: Supercyclic and chaotic translation semigroups publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-06960-0 – volume: 495 issue: 1 year: 2021 ident: 10.1016/j.jmaa.2024.128293_br0050 article-title: Γ-supercyclicity of families of translates in weighted Lp-spaces on locally compact groups publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2020.124709 – volume: 17 start-page: 793 issue: 4 year: 1997 ident: 10.1016/j.jmaa.2024.128293_br0140 article-title: Hypercyclic and chaotic semigroups of linear operators publication-title: Ergod. Theory Dyn. Syst. doi: 10.1017/S0143385797084976 – volume: 50 start-page: 107 issue: 1 year: 2003 ident: 10.1016/j.jmaa.2024.128293_br0150 article-title: Countably hypercyclic operators publication-title: J. Oper. Theory – volume: 78 start-page: 225 issue: 2 year: 2014 ident: 10.1016/j.jmaa.2024.128293_br0130 article-title: Cyclicity of vectors with orbital limit points for backward shifts publication-title: Integral Equ. Oper. Theory doi: 10.1007/s00020-013-2100-2 – volume: 244 start-page: 342 issue: 1 year: 2007 ident: 10.1016/j.jmaa.2024.128293_br0090 article-title: Hypercyclic behaviour of operators in a hypercyclic c0-semigroup publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2006.12.008 – volume: vol. 179 year: 2009 ident: 10.1016/j.jmaa.2024.128293_br0060 article-title: Dynamics of Linear Operators – volume: 67 start-page: 257 issue: 1 year: 2012 ident: 10.1016/j.jmaa.2024.128293_br0120 article-title: Hypercyclicity of shifts as a zero-one law of orbital limit points publication-title: J. Oper. Theory – volume: 110 start-page: 251 issue: 2 year: 2012 ident: 10.1016/j.jmaa.2024.128293_br0110 article-title: Szemerédi's theorem, frequent hypercyclicity and multiple recurrence publication-title: Math. Scand. doi: 10.7146/math.scand.a-15207 – volume: 270 start-page: 4443 issue: 12 year: 2016 ident: 10.1016/j.jmaa.2024.128293_br0080 article-title: Γ-supercyclicity publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2016.03.005 |
| SSID | ssj0011571 |
| Score | 2.4620788 |
| Snippet | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 128293 |
| SubjectTerms | Backward shift Hypercyclicity Orbital limit points Recurrence Supercyclicity Translation semigroup |
| Title | Orbits of the backward shifts with limit points |
| URI | https://dx.doi.org/10.1016/j.jmaa.2024.128293 |
| Volume | 537 |
| WOSCitedRecordID | wos001218979600001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0022-247X databaseCode: AIEXJ dateStart: 20211209 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0011571 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NT8MgGCa6edCD8TN-h4M3U20phXJczIya-HHQZLcGaImbrlu2uei_FwrtqplGD16alsLbj4fQp_C-zwvAsf6m8IiEyuNUcg8jjj2OZeghkvoCKyKwkEWyCXp7G3c67N7l2BwX6QRonsdvb2z4r1DrMg22CZ39A9yVUV2g9zXoeqth19tfAX83El3roGE4pTDzc2aqYPzUVWUs24uJajoZDrpOx2kOO-1Xcq6FmIBTLimUXWtL3rPFI_782h9Mi5F1qm_tfXZGWBfu1ogrPqlPMiBsPCJsmGXN6R_hIqt9NXBGVq7F9RBUGwYDsz4bzh2h7WRB77TX50b2CeHTWeXPcthfPlOV82Dpl9ZLjI3E2EisjUXQRDRicQM0W1ftznW1nBRENChl481TuOgp6-j39U7mM5Qa63hYA6sOENiyMK-DhSzfACs3FTjjTXBmAYcDBXUpLAGHFnBoAIcF4NACvgUeL9oP55eeS4PhydD3Jx5POUNKkMxHQoQ484X0GWf639OQ6TSWASLUBJFgJKSghKRcIBKpCAtEYxGG26CRD_JsB0B9xHCqKEeaOWqyGcdMMeGnUSBj4mdsFwTloyfSacSbVCUvyfcvfRecVG2GViHlx9pR-UYTx_Esd0t0B_mh3d6frrIPlme9-AA0JqPX7BAsyemkOx4dud7xASkBcLc |
| linkProvider | Elsevier |
| 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=Orbits+of+the+backward+shifts+with+limit+points&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Abakumov%2C+Evgeny&rft.au=Abbar%2C+Arafat&rft.date=2024-09-15&rft.issn=0022-247X&rft.volume=537&rft.issue=2&rft.spage=128293&rft_id=info:doi/10.1016%2Fj.jmaa.2024.128293&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jmaa_2024_128293 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon |