Mustafayev, HeybetkuluSevli, Hamdullah2025-05-102025-05-1020210022-247X1096-081310.1016/j.jmaa.2021.1250902-s2.0-85101545075https://doi.org/10.1016/j.jmaa.2021.125090https://hdl.handle.net/20.500.14720/7266Sevli, Hamdullah/0009-0003-0258-031XLet G be a locally compact abelian group and let M(G) be the convolution measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity, where mu(n) denotes nth convolution power of mu. We show that if mu is an element of M(G) is power bounded and A = [a(n,k)](n,k=0)(infinity) is a strongly regular matrix, then the limit lim(n ->infinity) Sigma(infinity)(k=0) a(n,k) mu(k) exists in the weak* topology of M(G) and is equal to the idempotent measure theta, where (theta) over cap = 1(int)F(mu). Here, (theta) over cap is the Fourier-Stieltjes transform of theta, F-mu :={gamma is an element of Gamma : (mu) over cap(gamma) = 1}, and 1(int) F-mu is the characteristic function of int F-mu. Some applications are also given. (C) 2021 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessLocally Compact (Abelian) GroupGroup AlgebraMeasure AlgebraConvolution OperatorRegular MatrixMean Ergodic TheoremArticle5001Q2Q2WOS:000634827700010