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

Author: S. S. Platonov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 933-947
MSC (2010): Primary 41A17; Secondary 42A10
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.

References [Enhancements On Off] (What's this?)

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Additional Information

S. S. Platonov
Affiliation: Petrozavodsk State University, pr. Lenina 33, Petrozavodsk 185910, Russia

Keywords: Approximation of functions, Jackson theorems, infinite-dimensional torus, harmonic analysis on compact Abelian groups
Received by editor(s): January 21, 2014
Published electronically: September 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society