Fejér Sums and Fourier Coefficients of Periodic Measures Full article
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Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362 |
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| Output data | Year: 2018, Volume: 98, Number: 2, Pages: 464-467 Pages count : 4 DOI: 10.1134/s1064562418060170 | ||||
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Abstract:
The Fejer sums of periodic measures and the norms of the deviations from the limit in the von Neumann ergodic theorem are calculating in terms of corresponding Fourier coefficients, in fact, using the same formulas. As a result, well-known estimates for the rates of convergence in the von Neumann ergodic theorem can be restated as estimates for the Fejer sums at a point for periodic measures. In this way, natural sufficient conditions for the polynomial growth and polynomial decay of these sums can be obtained in terms of Fourier coefficients. Besides, for example, it is shown that every continuous 2pi-periodic function is uniquely determined by its sequence of Fejer sums at any two points whose difference is incommensurable with pi.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
Fejér Sums and Fourier Coefficients of Periodic Measures
Doklady Mathematics. 2018. V.98. N2. P.464-467. DOI: 10.1134/s1064562418060170 WOS Scopus РИНЦ OpenAlex
Fejér Sums and Fourier Coefficients of Periodic Measures
Doklady Mathematics. 2018. V.98. N2. P.464-467. DOI: 10.1134/s1064562418060170 WOS Scopus РИНЦ OpenAlex
Original:
Качуровский A.Г.
, Подвигин И.В.
Суммы Фейера и коэффициенты Фурье периодических мер
Доклады академии наук. 2018. Т.482. №4. С.381-384. DOI: 10.31857/s086956520003086-7 РИНЦ MathNet OpenAlex
Суммы Фейера и коэффициенты Фурье периодических мер
Доклады академии наук. 2018. Т.482. №4. С.381-384. DOI: 10.31857/s086956520003086-7 РИНЦ MathNet OpenAlex
Identifiers:
| Web of science: | WOS:000449956100014 |
| Scopus: | 2-s2.0-85056359284 |
| Elibrary: | 38623788 |
| OpenAlex: | W2899623343 |