1 Ocak 2021 Dergi makalesi Açık Erişim

Mustafayev, Heybetkulu; Sevli, Hamdullah

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    <subfield code="a">Let 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 &amp;gt;= 0) parallel to mu(n)parallel to(1) &amp;lt; 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 -&amp;gt;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.</subfield>
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    <subfield code="a">Mean ergodic theorems for power bounded measures</subfield>
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    <subfield code="a">10.1016/j.jmaa.2021.125090</subfield>
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