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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 171–186 (Mi izv1612)  

This article is cited in 22 scientific papers (total in 22 papers)

Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions

V. N. Temlyakov


Abstract: This paper investigates the approximation of periodic functions of several variables by trigonometric polynomials whose harmonics lie in hyperbolic crosses. It is shown that in many cases the order of the widths, in the sense of Kolmogorov, can be found for classes of functions with a bounded mixed derivative or difference. The possibilities of linear methods of approximation are investigated.
Bibliography: 16 titles.

Full text: PDF file (1123 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 173–187

Bibliographic databases:

UDC: 517.9
MSC: 42A10, 42B99, 41A46, 41A63
Received: 27.11.1980

Citation: V. N. Temlyakov, “Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 171–186; Math. USSR-Izv., 20:1 (1983), 173–187

Citation in format AMSBIB
\Bibitem{Tem82}
\by V.~N.~Temlyakov
\paper Approximation of functions with a~bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 171--186
\mathnet{http://mi.mathnet.ru/izv1612}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643900}
\zmath{https://zbmath.org/?q=an:0511.42005|0499.42002}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 173--187
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001346}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Nikol'skii, “Aleksandrov and Kolmogorov in Dnepropetrovsk”, Russian Math. Surveys, 38:4 (1983), 41–55  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Temliakov V., “on the Approximation of Periodic-Functions of Many Variables”, 279, no. 2, 1984, 301–305  isi
    3. È. M. Galeev, “Kolmogorov widths in the space $\widetilde L_q$ of the classes $\widetilde W_p^{\overline\alpha}$ and $\widetilde H_p^{\overline\alpha}$ of periodic functions of several variables”, Math. USSR-Izv., 27:2 (1986), 219–237  mathnet  crossref  mathscinet  zmath
    4. V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions”, Math. USSR-Izv., 27:2 (1986), 285–322  mathnet  crossref  mathscinet  zmath
    5. V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Math. USSR-Sb., 56:1 (1987), 249–261  mathnet  crossref  mathscinet  zmath
    6. Belinskii E., “the Approximation of Periodic-Functions of Several-Variables By Floating System of Exponents and the Trigonometric Widths”, 284, no. 6, 1985, 1294–1297  isi
    7. Ðinh Dung, “Approximation by trigonometric polynomials of functions of several variables on the torus”, Math. USSR-Sb., 59:1 (1988), 247–267  mathnet  crossref  mathscinet  zmath
    8. V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Math. USSR-Izv., 28:1 (1987), 133–150  mathnet  crossref  mathscinet  zmath
    9. V. N. Temlyakov, “Estimates of the best bilinear approximations of functions of two variables and some of their applications”, Math. USSR-Sb., 62:1 (1989), 95–109  mathnet  crossref  mathscinet  zmath
    10. S. A. Nazarov, “Asymptotic solution of a variational inequality modelling a friction”, Math. USSR-Izv., 37:2 (1991), 337–369  mathnet  crossref  mathscinet  zmath  adsnasa
    11. I. I. Argatov, S. A. Nazarov, “Asymptotic analysis of problems on junctions of domains of different limit dimensions. A body pierced by a thin rod”, Izv. Math., 60:1 (1996), 1–37  mathnet  crossref  mathscinet  zmath  isi
    12. A. S. Romanyuk, “Approximability of the classes $B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations”, Sb. Math., 195:2 (2004), 237–261  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. E. M. Skorikov, “The information Kolmogorov width and some exact inequalities between widths”, Izv. Math., 71:3 (2007), 603–627  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Math. Notes, 82:2 (2007), 216–228  mathnet  crossref  crossref  mathscinet  isi  elib
    15. A. A. Vasileva, “Kolmogorovskie poperechniki vesovykh klassov Soboleva na kube”, Tr. IMM UrO RAN, 16, no. 4, 2010, 100–116  mathnet  elib
    16. Kudryavtsev S.N., “Generalized Haar series and their applications”, Anal Math, 37:2 (2011), 103–150  crossref  isi
    17. Vasil'eva A.A., “Kolmogorov Widths of Weighted Sobolev Classes on a Domain For a Special Class of Weights. II”, Russ. J. Math. Phys., 18:4 (2011), 465–504  crossref  isi
    18. Vasil'eva A.A., “Kolmogorov Widths of Weighted Sobolev Classes on a Domain For a Special Class of Weights”, Russ. J. Math. Phys., 18:3 (2011), 353–385  crossref  isi
    19. Pustovoitov N.N., “On the Kolmogorov widths of classes of functions with given mixed moduli of continuity”, Anal Math, 38:1 (2012), 41–64  crossref  isi
    20. A.A. Vasil’eva, “Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin”, Journal of Approximation Theory, 2012  crossref
    21. A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    22. A. A. Vasil’eva, “Widths of weighted Sobolev classes on a John domain: strong singularity at a point”, Rev Mat Complut, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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