Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle

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Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle. / Kachurovskii, A. G.; Lapshtaev, M. N.; Khakimbaev, A. J.

In: Siberian Electronic Mathematical Reports, Vol. 17, 2020, p. 1313-1321.

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

Harvard

Kachurovskii, AG, Lapshtaev, MN & Khakimbaev, AJ 2020, 'Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle', Siberian Electronic Mathematical Reports, vol. 17, pp. 1313-1321. https://doi.org/10.33048/semi.2020.17.097

APA

Kachurovskii, A. G., Lapshtaev, M. N., & Khakimbaev, A. J. (2020). Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle. Siberian Electronic Mathematical Reports, 17, 1313-1321. https://doi.org/10.33048/semi.2020.17.097

Vancouver

Kachurovskii AG, Lapshtaev MN, Khakimbaev AJ. Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle. Siberian Electronic Mathematical Reports. 2020;17:1313-1321. doi: 10.33048/semi.2020.17.097

Author

Kachurovskii, A. G. ; Lapshtaev, M. N. ; Khakimbaev, A. J. / Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle. In: Siberian Electronic Mathematical Reports. 2020 ; Vol. 17. pp. 1313-1321.

BibTeX

@article{68b17ae1437741dcbcbcd514d7f70b42,

title = "Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle",

abstract = "The Fejer sums for measures on the circle and the norms of the deviations from the limit in von Neumann's ergodic theorem are calculated, in fact, using the same formulas (by integrating the Fejer kernels) — and so, this ergodic theorem is a statement about the asymptotics of the Fejer sums at zero for the spectral measure of the corresponding dynamical system. It made it possible, having considered the integral Holder condition for signed measures, to prove a theorem that unifies both following well-known results: classical S.N. Bernstein's theorem on polynomial deviations of the Fejer sums for Holder functions — and theorem about polynomial rates of convergence in von Neumann's ergodic theorem.",

keywords = "deviations of Fejer sums, integral Holder condition, rates of convergence in von Neumann's ergodic theorem",

author = "Kachurovskii, {A. G.} and Lapshtaev, {M. N.} and Khakimbaev, {A. J.}",

year = "2020",

doi = "10.33048/semi.2020.17.097",

language = "English",

volume = "17",

pages = "1313--1321",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Von Neumann's Ergodic Theorem and Fejer Sums for Signed Measures on the Circle

AU - Kachurovskii, A. G.

AU - Lapshtaev, M. N.

AU - Khakimbaev, A. J.

PY - 2020

Y1 - 2020

N2 - The Fejer sums for measures on the circle and the norms of the deviations from the limit in von Neumann's ergodic theorem are calculated, in fact, using the same formulas (by integrating the Fejer kernels) — and so, this ergodic theorem is a statement about the asymptotics of the Fejer sums at zero for the spectral measure of the corresponding dynamical system. It made it possible, having considered the integral Holder condition for signed measures, to prove a theorem that unifies both following well-known results: classical S.N. Bernstein's theorem on polynomial deviations of the Fejer sums for Holder functions — and theorem about polynomial rates of convergence in von Neumann's ergodic theorem.

AB - The Fejer sums for measures on the circle and the norms of the deviations from the limit in von Neumann's ergodic theorem are calculated, in fact, using the same formulas (by integrating the Fejer kernels) — and so, this ergodic theorem is a statement about the asymptotics of the Fejer sums at zero for the spectral measure of the corresponding dynamical system. It made it possible, having considered the integral Holder condition for signed measures, to prove a theorem that unifies both following well-known results: classical S.N. Bernstein's theorem on polynomial deviations of the Fejer sums for Holder functions — and theorem about polynomial rates of convergence in von Neumann's ergodic theorem.

KW - deviations of Fejer sums

KW - integral Holder condition

KW - rates of convergence in von Neumann's ergodic theorem

UR - http://www.scopus.com/inward/record.url?scp=85099343848&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.097

DO - 10.33048/semi.2020.17.097

M3 - Article

AN - SCOPUS:85099343848

VL - 17

SP - 1313

EP - 1321

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 27504568