Continuous selections of Borel measures, positive operators and degenerate evolution problems

Francesco Altomare; Vita Leonessa

doi:10.33993/jnaat361-852

Authors

Francesco Altomare Universia degli Studi di Bari, Italy
Vita Leonessa Universia degli Studi della Basilicata, Italy

DOI:

https://doi.org/10.33993/jnaat361-852

Keywords:

degenerate differential operator, diffusion equation, Markov semigroup, Borel measure, positive approximation process, asymptotic formula

Abstract views: 214

Abstract

In this paper we continue the study of a sequence of positive linear operators which we have introduced in [9] and which are associated with a continuous selection of Borel measures on the unit interval. We show that the iterates of these operators converge to a Markov semigroup whose generator is a degenerate second-order elliptic differential operator on the unit interval. Some qualitative properties of the semigroup, or equivalently, of the solutions of the corresponding degenerate evolution problems, are also investigated.

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References

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