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Matematicheskie Zametki, 1977, Volume 22, Issue 2, Pages 285–295 (Mi mzm8049)  

This article is cited in 33 scientific papers (total in 33 papers)

Diameters of certain classes of analytic functions

L. V. Taikov

Moscow Institute of Forestry Engineering
Abstract: Exact values have been found, for the diameters in the sense of Kolmogorov of certain classes of functions with a Hardy metric, analytic in the unit circle, whose boundary values admit of a representation by a convolution or the averaged modulus of smoothness of their boundary values is majorized by a given function. In passing, certain extremal properties of trigonometric polynomials are established.
Received: 06.02.1976
English version:
Mathematical Notes, 1977, Volume 22, Issue 2, Pages 650–656
DOI: https://doi.org/10.1007/BF01780976
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: L. V. Taikov, “Diameters of certain classes of analytic functions”, Mat. Zametki, 22:2 (1977), 285–295; Math. Notes, 22:2 (1977), 650–656
Citation in format AMSBIB
\Bibitem{Tai77}
\by L.~V.~Taikov
\paper Diameters of certain classes of analytic functions
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 285--295
\mathnet{http://mi.mathnet.ru/mzm8049}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=466567}
\zmath{https://zbmath.org/?q=an:0382.30026}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 650--656
\crossref{https://doi.org/10.1007/BF01780976}
Linking options:
  • https://www.mathnet.ru/eng/mzm8049
  • https://www.mathnet.ru/eng/mzm/v22/i2/p285
  • This publication is cited in the following 33 articles:
    1. Sergіi Vakarchuk, Valentina Zabutna, Mikhailo Vakarchuk, “Userednenі kharakteristiki gladkostі v L2 ta otsіnki znachen poperechnikіv funktsіonalnikh klasіv”, Ukr. Mat. Zhurn., 77:2 (2025), 83  crossref
    2. M. Sh. Shabozov, A. A. Shabozova, “O sovmestnom priblizhenii nekotorykh klassov funktsii v prostranstve Bergmana B2”, Izv. vuzov. Matem., 2024, no. 6, 80–88  mathnet  crossref
    3. M. Sh. Shabozov, A. A. Shabozova, “On Simultaneous Approximation of Certain Classes of Functions in the Bergman Space B2”, Russ Math., 68:6 (2024), 68  crossref
    4. Mirgand Sh. Shabozov, Muqim S. Saidusajnov, “On widths of some classes of analytic functions in a circle”, Ural Math. J., 10:2 (2024), 121–130  mathnet  crossref
    5. M. Sh. Shabozov, A. A. Shabozova, “O tochnykh znacheniyakh poperechnikov klassov analiticheskikh v kruge funktsii”, Matem. tr., 27:4 (2024), 115–140  mathnet  crossref
    6. M. R. Langarshoev, “Nailuchshee priblizhenie i znacheniya poperechnikov nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana B2,γ”, Vestnik rossiiskikh universitetov. Matematika, 28:142 (2023), 182–192  mathnet  crossref
    7. M. Sh. Shabozov, “On the Best Simultaneous Approximation in the Bergman Space B2”, Math. Notes, 114:3 (2023), 377–386  mathnet  crossref  crossref  mathscinet
    8. M. Sh. Shabozov, “O nailuchshem sovmestnom priblizhenii funktsii v prostranstve Khardi”, Tr. IMM UrO RAN, 29, no. 4, 2023, 283–291  mathnet  crossref  elib
    9. M. Sh. Shabozov, Z. Sh. Malakbozov, “Sharp Jackson–Stechkin type inequalities in Hardy space H2 and widths of functional classes”, Ufa Math. J., 15:2 (2023), 74–84  mathnet  crossref
    10. M. Sh. Shabozov, G. A. Yusupov, “O nailuchshem polinomialnom priblizhenii funktsii v prostranstve Khardi Hq,R,(1q,R1)”, Chebyshevskii sb., 24:1 (2023), 182–193  mathnet  crossref
    11. M. Sh. Shabozov, Z. Sh. Malakbozov, “On the best polynomial approximation in Hardy space”, Russian Math. (Iz. VUZ), 66:11 (2022), 97–109  mathnet  crossref  crossref
    12. M. Sh. Shabozov, G. A. Yusupov, D. D. Zargarov, “O nailuchshei sovmestnoi polinomialnoi approksimatsii funktsii i ikh proizvodnykh v prostranstve Khardi”, Tr. IMM UrO RAN, 27, no. 4, 2021, 239–254  mathnet  crossref  elib
    13. S. B. Vakarchuk, “Estimates of the Values of n-Widths of Classes of Analytic Functions in the Weight Spaces H2,γ(D)”, Math. Notes, 108:6 (2020), 775–790  mathnet  crossref  crossref  mathscinet  isi  elib
    14. M. R. Langarshoev, “O nailuchshem polinomialnom priblizhenii funktsii v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 21:1 (2019), 27–36  mathnet  crossref  elib
    15. M. Sh. Shabozov, M. R. Langarshoev, “Best linear approximation methods for some classes of analytic functions on the unit disk”, Siberian Math. J., 60:6 (2019), 1101–1108  mathnet  crossref  crossref  isi  elib
    16. S.B. Vakarchuk, V.I. Zabutna, M.B. Vakarchuk, “The best polynomial approximations of some classes of analytic functions in the Hardy spaces”, Vìsn. Dnìpro unìv., Ser. Mat., 26:1 (2018), 8  crossref
    17. M. S. Saidusainov, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana”, Chebyshevskii sb., 17:1 (2016), 240–253  mathnet  elib
    18. M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in Hq,ρ, 1q, 0<ρ1”, Siberian Math. J., 57:2 (2016), 369–376  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Langarshoev M.R., “On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space”, Ukr. Math. J., 67:10 (2016), 1537–1551  crossref  mathscinet  isi  elib  scopus
    20. Vakarchuk S.B., Vakarchuk M.B., “Inequalities of Kolmogorov Type for Analytic Functions of One and Two Complex Variables and their Applications to Approximation Theory”, Ukr. Math. J., 63:12 (2012), 1795–1819  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
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