Fejer sums and Fourier coefficients of periodical measures

 
PIIS086956520003086-7-1
DOI10.31857/S086956520003086-7
Publication type Article
Status Published
Authors
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch of RAS
Novosibirsk State University
Address: Russian Federation, Novosibirsk
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch of RAS
Novosibirsk State University
Address: Russian Federation, Novosibirsk
Journal nameDoklady Akademii nauk
EditionVolume 482 Issue 4
Pages381-384
Abstract

The Fejer sums of periodical measures and the norms of the deviations from the limit in the von Neumann ergodic theorem both are calculating via corresponding Fourier coefficients, in fact, with the same formulas. It gives a possibility to rework well known results for the rates of convergence in the von Neumann ergodic theorem into the results for the Fejer sums at the point for periodical measures. We obtain this way some natural conditions for polynomial growth and polynomial degree of these sums in terms of Fourier coefficients. And obtain, for example, that every continuous 2п-periodical function is uniquely determined by its sequences of Fejer sums at any two points which difference is incommensurable with п.

Keywords
AcknowledgmentРабота выполнена при поддержке программы фундаментальных научных исследований СО РАН ќ I.1.2., проект ќ 0314-2016-0005.
Received10.11.2018
Publication date10.11.2018
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