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

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.

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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

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
2. Temliakov V., “on the Approximation of Periodic-Functions of Many Variables”, 279, no. 2, 1984, 301–305
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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
5. V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Math. USSR-Sb., 56:1 (1987), 249–261
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
7. Ðinh Dung, “Approximation by trigonometric polynomials of functions of several variables on the torus”, Math. USSR-Sb., 59:1 (1988), 247–267
8. V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Math. USSR-Izv., 28:1 (1987), 133–150
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
10. S. A. Nazarov, “Asymptotic solution of a variational inequality modelling a friction”, Math. USSR-Izv., 37:2 (1991), 337–369
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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
13. E. M. Skorikov, “The information Kolmogorov width and some exact inequalities between widths”, Izv. Math., 71:3 (2007), 603–627
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
15. A. A. Vasileva, “Kolmogorovskie poperechniki vesovykh klassov Soboleva na kube”, Tr. IMM UrO RAN, 16, no. 4, 2010, 100–116
16. Kudryavtsev S.N., “Generalized Haar series and their applications”, Anal Math, 37:2 (2011), 103–150
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
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
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
20. A.A. Vasil’eva, “Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin”, Journal of Approximation Theory, 2012
21. A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119
22. A. A. Vasil’eva, “Widths of weighted Sobolev classes on a John domain: strong singularity at a point”, Rev Mat Complut, 2013
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