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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1997, Volume 219, Pages 356–377 (Mi tm624)  

This article is cited in 27 scientific papers (total in 27 papers)

Representation and Approximation of Multivariate Periodic Functions with Bounded Mixed Moduli of Smoothness

S. Yongsheng, W. Heping
Received in June 1997
Bibliographic databases:
UDC: 517.518.823
Language: English
Citation: S. Yongsheng, W. Heping, “Representation and Approximation of Multivariate Periodic Functions with Bounded Mixed Moduli of Smoothness”, Approximation theory. Harmonic analysis, Collection of papers dedicated to the memory of Professor Sergei Borisovich Stechkin, Trudy Mat. Inst. Steklova, 219, Nauka, MAIK «Nauka», M., 1997, 356–377; Proc. Steklov Inst. Math., 219 (1997), 350–371
Citation in format AMSBIB
\Bibitem{YonHep97}
\by S.~Yongsheng, W.~Heping
\paper Representation and Approximation of Multivariate Periodic Functions with Bounded Mixed Moduli of Smoothness
\inbook Approximation theory. Harmonic analysis
\bookinfo Collection of papers dedicated to the memory of Professor Sergei Borisovich Stechkin
\serial Trudy Mat. Inst. Steklova
\yr 1997
\vol 219
\pages 356--377
\publ Nauka, MAIK «Nauka»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm624}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1642296}
\zmath{https://zbmath.org/?q=an:1032.42015}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 219
\pages 350--371
Linking options:
  • https://www.mathnet.ru/eng/tm624
  • https://www.mathnet.ru/eng/tm/v219/p356
  • This publication is cited in the following 27 articles:
    1. Fedunyk-Yaremchuk V O. Hembars'ka S.B., “Approximation of Classes of Periodic Functions of Several Variables With Given Majorant of Mixed Moduli of Continuity”, Carpathian Math. Publ., 13:3 (2021), 838–850  crossref  isi
    2. Duan L., Ye P., “Randomized Approximation Numbers on Besov Classes With Mixed Smoothness”, Int. J. Wavelets Multiresolut. Inf. Process., 18:4 (2020), 2050023  crossref  isi
    3. Yanchenko S.Ya., “Approximation of the Nikol'Skii-Besov Functional Classes By Entire Functions of a Special Form”, Carpathian Math. Publ., 12:1 (2020), 148–156  crossref  isi
    4. Duan L. Ye P., “Exact Asymptotic Orders of Various Randomized Widths on Besov Classes”, Commun. Pure Appl. Anal, 19:8 (2020), 3957–3971  crossref  isi
    5. Yanchenko S.Ya., Radchenko O.Ya., “Approximating Characteristics of the Nikol'Skii-Besov Classes (S1,Theta B)-B-R(R-D)”, Ukr. Math. J., 71:10 (2020), 1608–1626  crossref  isi
    6. Fedunyk-Yaremchuk O.V. Hembars'Kyi M.V. Hembars'Ka S.B., “Approximative Characteristics of the Nikol'Skii-Besov-Type Classes of Periodic Functions in the Space B-Infinity,B-1”, Carpathian Math. Publ., 12:2 (2020), 376–391  crossref  isi
    7. Fedunyk-Yaremchuk V O., Hembars'ka S.B., “Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_q$”, Carpathian Math. Publ., 11:2 (2019), 281–295  crossref  isi
    8. Pozhars'ka K.V., “Estimates For the Entropy Numbers of the Classes Bp, of Periodic Multivariable Functions in the Uniform Metric”, Ukr. Math. J., 70:9 (2019), 1439–1455  crossref  isi
    9. Sh. A. Balgimbayeva, T. I. Smirnov, “Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness”, Siberian Math. J., 59:2 (2018), 217–230  mathnet  crossref  crossref  isi  elib
    10. Balgimbayeva S. Smirnov T., “Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothnes”, Anal. Math., 43:1 (2017), 1–26  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Wang H., Wang K., “Optimal Recovery of Besov Classes of Generalized Smoothness and Sobolev Classes on the Sphere”, J. Complex., 32:1 (2016), 40–52  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Stasyuk S.A., “Best m-Term Trigonometric Approximation for Periodic Functions with Low Mixed Smoothness from the Nikol'skii–Besov-Type Classes”, Ukr. Math. J., 68:7 (2016), 1121–1145  crossref  mathscinet  isi  scopus  scopus
    13. Sh. A. Balgimbaeva, T. I. Smirnov, “Otsenki poperechnikov Fure klassov periodicheskikh funktsii so smeshannym modulem gladkosti”, Tr. IMM UrO RAN, 21, no. 4, 2015, 78–94  mathnet  mathscinet  elib
    14. Stasyuk S.A. Yanchenko S.Ya., “Approximation of Functions From Nikolskii-Besov Type Classes of Generalized Mixed Smoothness”, Anal. Math., 41:4 (2015), 311–334  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. S. A. Stasyuk, “Priblizhenie summami Fure i kolmogorovskie poperechniki klassov $\mathbf{MB}^\Omega_{p,\theta}$ periodicheskikh funktsii neskolkikh peremennykh”, Tr. IMM UrO RAN, 20, no. 1, 2014, 247–257  mathnet  mathscinet  elib
    16. A. F. Konograj, “Estimates of the Approximation Characteristics of the Classes $B^{\Omega}_{p,\theta}$ of Periodic Functions of Several Variables with Given Majorant of Mixed Moduli of Continuity”, Math. Notes, 95:5 (2014), 656–669  mathnet  crossref  crossref  mathscinet  isi  elib
    17. S. A. Stasyuk, “Nailuchshee priblizhenie periodicheskikh funktsii neskolkikh peremennykh iz klassov $MB^\omega_{p,\theta}$ v ravnomernoi metrike”, Tr. IMM UrO RAN, 18, no. 4, 2012, 258–266  mathnet  elib
    18. Wang H., Tang S., “Widths of Besov Classes of Generalized Smoothness on the Sphere”, J. Complex., 28:4 (2012), 468–488  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Duan L., Ye P., “Kolmogorov and Linear Widths on Generalized Besov Classes in the Monte Carlo Setting”, Theoretical and Mathematical Foundations of Computer Science, Communications in Computer and Information Science, 164, ed. Zhou Q., Springer-Verlag Berlin, 2011, 70–76  crossref  zmath  isi  scopus  scopus
    20. S. A. Stasyuk, “Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$”, Math. Notes, 87:1 (2010), 102–114  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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