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Sur le comportement asymptotique des puissances de convolution d’une probabilité. (French) Zbl 0536.60014

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.

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.
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