On summability of pairs of convolution sequences of probability measures on locally compact semigroups
The paper is concerned with the summability of convolution powers \(\mu^i*\nu^j\) of probabilities on a locally compact topological semigroup. Continuing previous investigations, the authors consider sequences \((A_n)_{n\geq 1}\) of non-negative matrices. A pair \((\mu,s)\) of probabilities is (weakly resp. vaguely) \((A_n)\)-summable to a measure \(\lambda\) if \(\sum_{i,j\geq 1} a_{ij}^{(n)} \mu_i*\nu^j\) converges (weakly resp. vaguely) to \(\lambda\). The authors obtain conditions for weak (resp. vague) summability.
scientific article; zbMATH DE number 1239701