Mustafayev, HeybetkuluTopal, Hayri2025-05-102025-05-1020210010-13541730-630210.4064/cm8214-6-20202-s2.0-85107159870https://doi.org/10.4064/cm8214-6-2020https://hdl.handle.net/20.500.14720/7185Let 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).eninfo:eu-repo/semantics/closedAccessLocally Compact Abelian GroupGroup AlgebraMeasure AlgebraConvolution OperatorConvergenceArticle1652Q4Q3321340WOS:000652831100009