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Mathematics of the USSR-Sbornik, 1982, Volume 41, Issue 1, Pages 53–66
DOI: https://doi.org/10.1070/SM1982v041n01ABEH002220 (Mi sm2778) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Approximation of periodic functions of several variables with bounded mixed difference

V. N. Temlyakov
English version PDF (577 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM1982v041n01ABEH002220
Abstract: This paper studies questions concerning the approximation of functions of several variables by trigonometric polynomials whose harmonics lie in a “hyperbolic cross” and also properties of functions which do not have harmonics lying in a “hyperbolic cross”. Analogues of H. Bohr's inequality are obtained for such functions. Estimates of optimal order are obtained for the upper bounds of best approximations of certain classes of functions, defined using mixed differences, by trigonometric polynomials whose harmonics lie in a “hyperbolic cross”. The diameters of certain classes are found.
Bibliography: 13 titles.
Received: 14.02.1980
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1980, Volume 113(155), Number 1(9), Pages 65–80
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 42B99
Language: English
Original paper language: Russian
Citation: V. N. Temlyakov, “Approximation of periodic functions of several variables with bounded mixed difference”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 65–80; Math. USSR-Sb., 41:1 (1982), 53–66
Citation in format AMSBIB
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\paper Approximation of periodic functions of several variables with bounded mixed difference
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\yr 1980
\vol 113(155)
\issue 1(9)
\pages 65--80
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\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 1
\pages 53--66
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:552
    Russian version PDF:203
    English version PDF:15
    References:67
    First page:1
     
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