Mustafayev, Heybetkulu2024-07-122024-07-122019Mustafayev, H. (2019).Norm and almost everywhere convergence of convolution powers. International Conference of Mathematical Sciences (ICMS 2019). s. 42.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2174Let G be a locally compact abelian group with the dual group ?, M (G), the measure algebra of G, and Mr (G), the largest regular subalgebra of M (G). For a power bounded measure µ ? M (G), we put Fµ = {? ? ? : µb (?) = 1} and Eµ = {? ? ? : |µb (?)| = 1} , where µb is the Fourier-Stieltjes transform of µ. Let (?, ?, m) be a ??finite positive measure space and let ? = {?g}g?G be an action of G in (?, ?, m) by invertible measure preserving transformations. Any action ? induces a representation T = {Tg}g?G of G on L p (?) (1 ? p < ?) by invertible isometries, where (Tgf) (?) = f (?g?). If ? is continuous, then for any µ ? M (G), we can define a bounded linear operator on L p (?) (1 ? p < ?) associated with µ, denoted by Tµ, which integrates Tg with respect to µ. Theorem. Let µ ? Mr (G) be power bounded and 1 < p < ?. If Fµ = Eµ, then the sequence { Tn µ f } converges strongly for every f ? L p (G).enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessAbelian groupMeasure algebraL p -spaceConvergenceArticle4242