Ukrainian Mathematical Journal

, Volume 48, Issue 1, pp 90–100 | Cite as

Approximation of classes of functions of many variables by their orthogonal projections onto subspaces of trigonometric polynomials

  • A. S. Romanyuk
Article

Abstract

In the spaceL q, 1<q<∞ we establish estimates for the orders of the best approximations of the classes of functions of many variablesB 1,θ r andB p r by orthogonal projections of functions from these classes onto the subspaces of trigonometric polynomials. It is shown that, in many cases, the estimates obtained in the present work are better in order than in the case of approximation by polynomials with harmonics from the hyperbolic cross.

Keywords

Periodic Function Orthogonal Projection Trigonometric Polynomial Ukrainian Academy Mixed Derivative 

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Copyright information

© Plenum Publishing Corporation 1997

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  • A. S. Romanyuk

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