Direct and inverse theorems in approximation theory for periodic functions in S.B. Stechkin’s papers and the development of these theorems
S.B. Stechkin made a considerable contribution to the important aspect of approximation theory for periodic functions concerned with direct and inverse theorems. We present the history of developing this research area and pose new problems.
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| Published in: | Proceedings of the Steklov Institute of Mathematics Vol. 273; no. Suppl 1; pp. 1 - 13 |
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| Format: | Journal Article |
| Language: | English |
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SP MAIK Nauka/Interperiodica
01.07.2011
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| ISSN: | 0081-5438, 1531-8605 |
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| Abstract | S.B. Stechkin made a considerable contribution to the important aspect of approximation theory for periodic functions concerned with direct and inverse theorems. We present the history of developing this research area and pose new problems. |
|---|---|
| AbstractList | S.B. Stechkin made a considerable contribution to the important aspect of approximation theory for periodic functions concerned with direct and inverse theorems. We present the history of developing this research area and pose new problems. |
| Author | Ivanov, V. I. |
| Author_xml | – sequence: 1 givenname: V. I. surname: Ivanov fullname: Ivanov, V. I. email: ivaleryi@mail.ru organization: Tula State University |
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| Cites_doi | 10.1007/BF02537726 10.1007/s00365-008-9039-6 10.1007/BF01908905 10.4213/rm1558 10.1006/jath.1994.1040 10.4213/sm838 10.1215/S0012-7094-37-00342-9 10.1215/S0012-7094-45-01206-3 |
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| Issue | Suppl 1 |
| Keywords | Jackson-Stechkin inequality modulus of continuity inverse inequality best approximation |
| Language | English |
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| References | BariN. K.StechkinS. B.Trudy Moskov. Mat. O-va195654830072.05702 BerdyshevV. I.Trudy Mat. Inst. Steklova19678830162.36201 IvanovV. I.Mat. Zametki19751856414127100337.42001 AkhiezerN. I.Lectures on Approximation Theory1947MoscowGostekhizdat0031.15704 KozkoA. I.RozhdestvenskiiA. V.Mat. Sb.2004195832101337 StechkinS. B.Dokl Akad. Nauk. SSSR19496521350038.21503 ChernykhN. I.Trudy Mat. Inst. Steklova1992198232 ZygmundA.Unic. Nac. Tucuman Revista. A19507259424790040.18101 KolomoitsevYu. S.Ukr. Mat. Zh.20075991221239698910.1007/s11253-007-0092-2 StechkinS. B.Selected Works: Mathematics1998MoscowNauka0923.41002 RadoslavovaT. V.Anal. Math.197952195492390432.4101610.1007/BF01908905 de la Vallée PoussinC. J.Leçons sur l’Approximation des Fonctions d’Une Variable Réelle1919ParisGauthier-VillarsJFM 47.0908.02 ZygmundA.Duke Math. J.19451247126910060.1380610.1215/S0012-7094-45-01206-3 StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.19511532190042.30001 RieszM.Jahresber. Deutsch. Math.-Verein.191423354 StorozhenkoE. A.KrotovV. G.Osval’dP.Mat. Sb.1975983395402384 BernsteinS. N.Dokl. Akad. Nauk SSSR1947572111 IvanovV. I.SmirnovO. I.Jackson’s Constants and Young’s Constants in Spaces Lp1995TulaTul’sk. Gos. Univ. ChernykhN. I.Mat. Zametki196725513221187 KorneichukN. P.Dokl. Akad. Nauk SSSR19621453514150524 NatansonG. I.TimanM. F.Vestn. Leningr. Gos. Univ.197931950564575 QuadeE. S.Duke Math. J.1937352915460080017.2050110.1215/S0012-7094-37-00342-9 FoucartS.KryakinYu.ShadrinA.Constr. Approx.200929215724815871181.4101710.1007/s00365-008-9039-6 RunovskiiK. V.Dokl. Ross. Akad. Nauk19933315684 TimanM. F.Approximation and Properties of Periodic Functions2009KievNauk. Dumka SalemR.C. R. Acad. Sci.1935201703 ChernykhN. I.Trudy Mat. Inst. Steklova19678871 StorozhenkoE. A.Osval’dP.Sib. Mat. Zh.19781948880395.41016 Vasil’evS. N.Trudy Inst. Mat. Mekh. UrO RAN20017175 RunovskiiK. V.Mat. Sb.1994185881 TimanM. F.Mat. Sb.1958461125100198 TimanM. F.Ukr. Mat. Zh.19661811341948280198.0930110.1007/BF02537726 StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.19531764990052.06101 BabenkoA. G.Trudy Inst. Mat. Mekh. UrO RAN20017130 Il’yasovN. A.Dokl. Akad. Nauk SSSR198427661301753368 StechkinS. B.Trudy Mat. Inst. Steklova196788170167.33601 GeitV. E.Izv. Vyssh. Uchebn. Zaved., Ser. Mat.1972467310520 Nikol’skiiS. M.Dokl. Akad. Nauk SSSR19486091507 D. Jackson, Dissertation (Göttingen, 1911). RathoreR. K. S.J. Approx. Theory.19947715312759310809.4102510.1006/jath.1994.1040 TimanA. F.TimanM. F.Dokl. Akad. Nauk SSSR19507117348670035.16302 TimanA. F.Theory of Approximation of Functions of a Real Variable1960MoscowFizmatgiz StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.1956202197776930070.06501 ArestovV. V.BerdyshevV. I.SubbotinYu. N.ChernykhN. I.Trudy Inst. Mat. Mekh. UrO RAN19964314839281059.41500 GeitV. E.Mat. Zametki1971105571294971 BernsteinS. N.Soobshch. Khar’k. Mat. O-va, Ser. 219121349 BesovO. V.BukhshtaberV. M.VitushkinA. G.Uspekhi Mat. Nauk199651631440153 RunovskiiK. V.Mat. Sb.1993184233 StechkinS. B.Trudy Mat. Inst. Steklova196162480106.27501 KonyaginS. V.TelyakovskiiS. A.Fundam. Prikl. Mat.19973495517944930927.01038 M. F. Timan, in Scientific Conf. of the Dnepropetrovsk Agricultural Institute (Promin’, Dnepropetrovsk, 1965), pp. 62–65 [in Russian]. TrigubR. M.Izv. Akad. Nauk SSSR, Ser. Mat.19652936151795310145.29401 IvanovV. I.Mat. Zametki199456215 LozinskiiS. M.Dokl. Akad. Nauk SSSR195283564547177 StechkinS. B.Dokl. Akad. Nauk SSSR194860915110034.03801 TimanM. F.Research on Modern Problems of Constructive Functional Analysis1965BakuAkad. Nauk Azerb. SSR1825 V. I. Ivanov (6345_CR10) 1975; 18 E. S. Quade (6345_CR49) 1937; 3 E. A. Storozhenko (6345_CR34) 1975; 98 K. V. Runovskii (6345_CR22) 1994; 185 R. M. Trigub (6345_CR43) 1965; 29 6345_CR48 S. N. Bernstein (6345_CR6) 1947; 57 O. V. Besov (6345_CR31) 1996; 51 M. F. Timan (6345_CR41) 1966; 18 6345_CR40 S. M. Nikol’skii (6345_CR19) 1948; 60 S. B. Stechkin (6345_CR29) 1967; 88 A. I. Kozko (6345_CR14) 2004; 195 S. B. Stechkin (6345_CR24) 1949; 65 M. Riesz (6345_CR52) 1914; 23 C. J. Vallée Poussin de la (6345_CR54) 1919 M. F. Timan (6345_CR39) 1965 A. F. Timan (6345_CR37) 1950; 71 N. I. Akhiezer (6345_CR1) 1947 M. F. Timan (6345_CR38) 1958; 46 A. G. Babenko (6345_CR2) 2001; 7 A. Zygmund (6345_CR56) 1950; 7 S. B. Stechkin (6345_CR25) 1951; 15 A. Zygmund (6345_CR55) 1945; 12 V. I. Berdyshev (6345_CR4) 1967; 88 S. B. Stechkin (6345_CR27) 1956; 20 G. I. Natanson (6345_CR18) 1979; 3 V. V. Arestov (6345_CR32) 1996; 4 M. F. Timan (6345_CR42) 2009 R. Salem (6345_CR53) 1935; 201 N. K. Bari (6345_CR3) 1956; 5 V. I. Ivanov (6345_CR11) 1994; 56 N. I. Chernykh (6345_CR44) 1967; 88 S. V. Konyagin (6345_CR33) 1997; 3 K. V. Runovskii (6345_CR21) 1993; 331 N. I. Chernykh (6345_CR46) 1992; 198 E. A. Storozhenko (6345_CR35) 1978; 19 S. B. Stechkin (6345_CR23) 1948; 60 S. Foucart (6345_CR47) 2009; 29 K. V. Runovskii (6345_CR20) 1993; 184 S. N. Vasil’ev (6345_CR7) 2001; 7 V. E. Geit (6345_CR9) 1972; 4 Yu. S. Kolomoitsev (6345_CR15) 2007; 59 N. A. Il’yasov (6345_CR13) 1984; 276 S. B. Stechkin (6345_CR28) 1961; 62 A. F. Timan (6345_CR36) 1960 N. I. Chernykh (6345_CR45) 1967; 2 N. P. Korneichuk (6345_CR16) 1962; 145 R. K. S. Rathore (6345_CR51) 1994; 77 S. N. Bernstein (6345_CR5) 1912; 13 S. B. Stechkin (6345_CR26) 1953; 17 S. B. Stechkin (6345_CR30) 1998 T. V. Radoslavova (6345_CR50) 1979; 5 V. E. Geit (6345_CR8) 1971; 10 S. M. Lozinskii (6345_CR17) 1952; 83 V. I. Ivanov (6345_CR12) 1995 |
| References_xml | – reference: FoucartS.KryakinYu.ShadrinA.Constr. Approx.200929215724815871181.4101710.1007/s00365-008-9039-6 – reference: Vasil’evS. N.Trudy Inst. Mat. Mekh. UrO RAN20017175 – reference: LozinskiiS. M.Dokl. Akad. Nauk SSSR195283564547177 – reference: TimanA. F.TimanM. F.Dokl. Akad. Nauk SSSR19507117348670035.16302 – reference: NatansonG. I.TimanM. F.Vestn. Leningr. Gos. Univ.197931950564575 – reference: ChernykhN. I.Trudy Mat. Inst. Steklova19678871 – reference: IvanovV. I.SmirnovO. I.Jackson’s Constants and Young’s Constants in Spaces Lp1995TulaTul’sk. Gos. Univ. – reference: TimanM. F.Mat. Sb.1958461125100198 – reference: ChernykhN. I.Mat. Zametki196725513221187 – reference: BariN. K.StechkinS. B.Trudy Moskov. Mat. O-va195654830072.05702 – reference: SalemR.C. R. Acad. Sci.1935201703 – reference: M. F. Timan, in Scientific Conf. of the Dnepropetrovsk Agricultural Institute (Promin’, Dnepropetrovsk, 1965), pp. 62–65 [in Russian]. – reference: StorozhenkoE. A.KrotovV. G.Osval’dP.Mat. Sb.1975983395402384 – reference: BernsteinS. N.Soobshch. Khar’k. Mat. O-va, Ser. 219121349 – reference: StechkinS. B.Trudy Mat. Inst. Steklova196162480106.27501 – reference: StorozhenkoE. A.Osval’dP.Sib. Mat. Zh.19781948880395.41016 – reference: StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.1956202197776930070.06501 – reference: RunovskiiK. V.Dokl. Ross. Akad. Nauk19933315684 – reference: RunovskiiK. V.Mat. Sb.1993184233 – reference: BesovO. V.BukhshtaberV. M.VitushkinA. G.Uspekhi Mat. Nauk199651631440153 – reference: BerdyshevV. I.Trudy Mat. Inst. Steklova19678830162.36201 – reference: RathoreR. K. S.J. Approx. Theory.19947715312759310809.4102510.1006/jath.1994.1040 – reference: AkhiezerN. I.Lectures on Approximation Theory1947MoscowGostekhizdat0031.15704 – reference: RunovskiiK. V.Mat. Sb.1994185881 – reference: TimanM. F.Research on Modern Problems of Constructive Functional Analysis1965BakuAkad. Nauk Azerb. SSR1825 – reference: TimanM. F.Ukr. Mat. Zh.19661811341948280198.0930110.1007/BF02537726 – reference: StechkinS. B.Trudy Mat. Inst. Steklova196788170167.33601 – reference: GeitV. E.Mat. Zametki1971105571294971 – reference: StechkinS. B.Dokl. Akad. Nauk SSSR194860915110034.03801 – reference: Il’yasovN. A.Dokl. Akad. Nauk SSSR198427661301753368 – reference: Nikol’skiiS. M.Dokl. Akad. Nauk SSSR19486091507 – reference: StechkinS. B.Selected Works: Mathematics1998MoscowNauka0923.41002 – reference: TrigubR. M.Izv. Akad. Nauk SSSR, Ser. Mat.19652936151795310145.29401 – reference: KonyaginS. V.TelyakovskiiS. A.Fundam. Prikl. Mat.19973495517944930927.01038 – reference: IvanovV. I.Mat. Zametki199456215 – reference: KorneichukN. P.Dokl. Akad. Nauk SSSR19621453514150524 – reference: BabenkoA. G.Trudy Inst. Mat. Mekh. UrO RAN20017130 – reference: KozkoA. I.RozhdestvenskiiA. V.Mat. Sb.2004195832101337 – reference: RieszM.Jahresber. Deutsch. Math.-Verein.191423354 – reference: QuadeE. S.Duke Math. J.1937352915460080017.2050110.1215/S0012-7094-37-00342-9 – reference: StechkinS. B.Dokl Akad. Nauk. SSSR19496521350038.21503 – reference: StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.19511532190042.30001 – reference: TimanM. F.Approximation and Properties of Periodic Functions2009KievNauk. Dumka – reference: ArestovV. V.BerdyshevV. I.SubbotinYu. N.ChernykhN. I.Trudy Inst. Mat. Mekh. UrO RAN19964314839281059.41500 – reference: ZygmundA.Unic. Nac. Tucuman Revista. A19507259424790040.18101 – reference: RadoslavovaT. V.Anal. Math.197952195492390432.4101610.1007/BF01908905 – reference: ZygmundA.Duke Math. J.19451247126910060.1380610.1215/S0012-7094-45-01206-3 – reference: KolomoitsevYu. S.Ukr. Mat. Zh.20075991221239698910.1007/s11253-007-0092-2 – reference: BernsteinS. N.Dokl. Akad. Nauk SSSR1947572111 – reference: GeitV. E.Izv. Vyssh. Uchebn. Zaved., Ser. Mat.1972467310520 – reference: TimanA. F.Theory of Approximation of Functions of a Real Variable1960MoscowFizmatgiz – reference: ChernykhN. I.Trudy Mat. Inst. Steklova1992198232 – reference: IvanovV. I.Mat. Zametki19751856414127100337.42001 – reference: StechkinS. B.Izv. Akad. Nauk SSSR, Ser. Mat.19531764990052.06101 – reference: D. Jackson, Dissertation (Göttingen, 1911). – reference: de la Vallée PoussinC. J.Leçons sur l’Approximation des Fonctions d’Une Variable Réelle1919ParisGauthier-VillarsJFM 47.0908.02 – volume: 65 start-page: 135 issue: 2 year: 1949 ident: 6345_CR24 publication-title: Dokl Akad. Nauk. SSSR – volume: 88 start-page: 71 year: 1967 ident: 6345_CR44 publication-title: Trudy Mat. Inst. Steklova – volume: 18 start-page: 134 issue: 1 year: 1966 ident: 6345_CR41 publication-title: Ukr. Mat. Zh. doi: 10.1007/BF02537726 – volume: 4 start-page: 3 year: 1996 ident: 6345_CR32 publication-title: Trudy Inst. Mat. Mekh. UrO RAN – volume: 88 start-page: 3 year: 1967 ident: 6345_CR4 publication-title: Trudy Mat. 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| Title | Direct and inverse theorems in approximation theory for periodic functions in S.B. Stechkin’s papers and the development of these theorems |
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