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

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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 r1,θ andB r p,α 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.

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Authors
  1. A. S. Romanyuk
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Romanyuk, A.S. Approximation of classes of functions of many variables by their orthogonal projections onto subspaces of trigonometric polynomials. Ukr Math J 48, 90–100 (1996). https://doi.org/10.1007/BF02390986

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  • DOI: https://doi.org/10.1007/BF02390986

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