Abstract: The Fejér sums of periodic measures and the norms of the deviations from the limit in the von Neumann ergodic theorem are calculated, in fact, using the same formulas (by integrating the Fejér kernels), so this ergodic theorem is, in fact, a statement about the asymptotics of the growth of the Fejér sums at zero for the spectral measure of the corresponding dynamical system. As a result, well-known estimates for the rates of convergence in the von Neumann ergodic theorem can be restated as estimates of the Fejér sums at the point for periodic measures. For example, natural criteria for the polynomial growth and polynomial decrease in these sums can be obtained. On the contrary, available in the literature, numerous estimates for the deviations of Fejér sums at a point can be used to obtain new estimates for the rate of convergence in this ergodic theorem. © 2018, Pleiades Publishing, Ltd.

Cite: Kachurovskii A.G. , Podvigin I.V.
Fejér Sums for Periodic Measures and the von Neumann Ergodic Theorem
Doklady Mathematics. 2018. V.98. N1. P.344-347. DOI: 10.1134/S1064562418050149 WOS Scopus РИНЦ OpenAlex

Original: Качуровский A.Г. , Подвигин И.В.
Суммы Фейера периодических мер и эргодическая теорема фон Неймана
Доклады академии наук. 2018. Т.481. №4. С.358-361. DOI: 10.31857/s086956520001688-9 РИНЦ MathNet OpenAlex

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Web of science:	WOS:000443716900013
Scopus:	2-s2.0-85052864934
Elibrary:	35721604
OpenAlex:	W2890498349

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Web of science	2
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