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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.
в: Siberian Electronic Mathematical Reports, Том 17, 2020, стр. 1313-1321.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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.
N1 - Publisher Copyright: © 2020. All Rights Reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
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