Fejer sums and Fourier coefficients of periodical measures

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

Acknowledgment

Работа выполнена при поддержке программы фундаментальных научных исследований СО РАН ќ I.1.2., проект ќ 0314-2016-0005.

Received

10.11.2018

Publication date

10.11.2018

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GOST	Kachurovskii A., Podvigin I. Fejer sums and Fourier coefficients of periodical measures // Doklady Akademii nauk – 2018. – V. 482. – Issue 4 C. 381-384 [Electronic resource]. URL: http://ras.jes.su/dan/s086956520003086-7-1-en (circulation date: 26.04.2024). DOI: 10.31857/S086956520003086-7
MLA	Kachurovskii, A., Podvigin, I. "Fejer sums and Fourier coefficients of periodical measures." Doklady Akademii nauk 482.4 (2018):381-384. DOI: 10.31857/S086956520003086-7
APA	Kachurovskii A., Podvigin I. (2018). Fejer sums and Fourier coefficients of periodical measures. Doklady Akademii nauk 482(4), pp.381-384 DOI: 10.31857/S086956520003086-7

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