Derriennic, Y.; Lin, M. Sur le comportement asymptotique des puissances de convolution d’une probabilité. (French) Zbl 0536.60014 Ann. Inst. Henri Poincaré, Probab. Stat. 20, 127-132 (1984). Summary: Given a regular probability measure \(\mu\) on a locally compact Abelian group, we develop equivalent conditions to the \(L^ p\)-strong convergence to 0 of the convolution operators \(\mu^ n\), with \(p=1\) or \(p>1\). We use only general methods of the theory of Markov operators and elementary facts of harmonic analysis. Cited in 7 Documents MSC: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 60J35 Transition functions, generators and resolvents 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A10 Measure algebras on groups, semigroups, etc. Keywords:locally compact Abelian group; convolution operators; harmonic analysis PDFBibTeX XMLCite \textit{Y. Derriennic} and \textit{M. Lin}, Ann. Inst. Henri Poincaré, Probab. Stat. 20, 127--132 (1984; Zbl 0536.60014) Full Text: Numdam EuDML