Fejér Sums and Fourier Coefficients of Periodic Measures

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Fejér Sums and Fourier Coefficients of Periodic Measures. / Kachurovskii, A. G.; Podvigin, I. V.

In: Doklady Mathematics, Vol. 98, No. 2, 01.09.2018, p. 464-467.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{52908471d24842fab6eeefaf9ddd01f7,

title = "Fej{\'e}r Sums and Fourier Coefficients of Periodic Measures",

abstract = "The Fej{\'e}r 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 Fej{\'e}r 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 2π-periodic function is uniquely determined by its sequence of Fej{\'e}r sums at any two points whose difference is incommensurable with π.",

keywords = "ERGODIC-THEOREMS, CONVERGENCE, RATES",

author = "Kachurovskii, {A. G.} and Podvigin, {I. V.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = sep,

day = "1",

doi = "10.1134/S1064562418060170",

language = "English",

volume = "98",

pages = "464--467",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Fejér Sums and Fourier Coefficients of Periodic Measures

AU - Kachurovskii, A. G.

AU - Podvigin, I. V.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - The Fejér 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 Fejér 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 2π-periodic function is uniquely determined by its sequence of Fejér sums at any two points whose difference is incommensurable with π.

AB - The Fejér 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 Fejér 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 2π-periodic function is uniquely determined by its sequence of Fejér sums at any two points whose difference is incommensurable with π.

KW - ERGODIC-THEOREMS

KW - CONVERGENCE

KW - RATES

UR - http://www.scopus.com/inward/record.url?scp=85056359284&partnerID=8YFLogxK

U2 - 10.1134/S1064562418060170

DO - 10.1134/S1064562418060170

M3 - Article

AN - SCOPUS:85056359284

VL - 98

SP - 464

EP - 467

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 17415169