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On summability of pairs of convolution sequences of probability measures on locally compact semigroups

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Abstract

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

$$\left( {\mathop \Sigma \limits_{i = 1}^\infty \mathop \Sigma \limits_{j = 1}^\infty a_{ij}^{(n)} \mu ^i *v^j ,n \in \mathbb{N}} \right)$$

where μ and ν are probability measures on locally compact commutative semigroupS andA n =[a (n) ij (i, j, n ɛ N) are double stochastic matrices satisfying some additional conditions. Our results generalize the results in [9]. Theorem 1 also holds if we make some changes on the topological assumptions onS, i.e. if we suppose thatS is a polish space.

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Authors and Affiliations

  1. Department of Mathematics, University of Rijeka, Omladinska 14, 61000, Rijeka, Croatia

    Cvetan Jardas

  2. Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000, Zagreb, Croatia

    Josip Pečarić

  3. Department of Mathematics, University of Zagreb, Bijenicka 30, 10000, Zagreb, Croatia

    Nikola Sarapa

Authors
  1. Cvetan Jardas
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  2. Josip Pečarić
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  3. Nikola Sarapa
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Jardas, C., Pečarić, J. & Sarapa, N. On summability of pairs of convolution sequences of probability measures on locally compact semigroups. Rend. Circ. Mat. Palermo 47, 481–492 (1998). https://doi.org/10.1007/BF02851394

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  • DOI: https://doi.org/10.1007/BF02851394

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