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ERGODIC PROPERTIES OF CONVOLUTION OPERATORS IN GROUP ALGEBRAS

   Mustafayev, Heybetkulu; Topal, Hayri

Let G be a locally compact abelian group and let L-1 (G) and M(G) be respectively the group algebra and the convolution measure algebra of G. For mu is an element of M(G), let T(mu)f = mu * f be the convolution operator on L-1(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 the nth convolution power of mu. We study some ergodic properties of the convolution operator T-mu, in the case when mu is power bounded. We also present some results concerning almost everywhere convergence of the sequence {T(mu)(n)f} in L-1 (G).

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Mustafayev, H. ve Topal, H. (2021). ERGODIC PROPERTIES OF CONVOLUTION OPERATORS IN GROUP ALGEBRAS. COLLOQUIUM MATHEMATICUM, 165(2), 321–340. doi:10.4064/cm8214-6-2020

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