Certain approximation problems for functions on the infinite-dimensional torus: Analogs of the Jackson theorem

Platonov, S.

doi:10.1090/spmj/1368

Certain approximation problems for functions on the infinite-dimensional torus: Analogs of the Jackson theorem
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by S. S. Platonov
Translated by: S. Kislyakov

St. Petersburg Math. J. 26 (2015), 933-947

DOI: https://doi.org/10.1090/spmj/1368

Published electronically: September 21, 2015

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Abstract:

Approximation of functions on the infinite-dimensional torus by trigonometric polynomials is treated. The main results of the paper provide analogs of the Jackson theorem about estimates of the best approximation in terms of the modulus of continuity of a function.

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