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Journal of Soviet Mathematics

, Volume 28, Issue 3, pp 294–305 | Cite as

Approximation of functions from B p, θ l (G) by anisotropic averages

  • V. P. Il'in
Article

Abstract

The article considers the approximation of functions from O. V. Besov's class B p, θ l (G) by anisotropic average functions. Proofs are given of the approximation theorem, the inverse theorem of approximation theory, and the saturation theorem associated with the choice of the averaging kernel.

Keywords

Average Function Approximation Theory Approximation Theorem Average Kernel Anisotropic Average 
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Literature cited

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    O. V. Besov, “Investigating a family of functional spaces in connection with embedding and continuation theorems,” Tr. Mat. Inst. Akad. Nauk SSSR,60, 42–81 (1961).Google Scholar
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    O. V. Besov, V. P. Il'in, and S.M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Moscow (1975).Google Scholar
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    K. K. Golovkin, “On approximation of functions in arbitrary norms,” Tr. Mat. Inst., Akad, Nauk SSSR,70, 26–37 (1964).Google Scholar
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    H. Shapiro, “Smoothing and approximation of functions,” Metsci. Report,55, 109 (1967).Google Scholar
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    S. M. Nikol'skii, Approximation of Functions of Many Variables and Embedding Theorems [in Russian], Moscow (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. P. Il'in

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