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

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...

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Bibliographic Details
Published inJournal of numerical analysis and approximation theory Vol. 36; no. 1
Main Authors Francesco Altomare, Vita Leonessa
Format Journal Article
LanguageEnglish
Published Publishing House of the Romanian Academy 01.02.2007
Subjects
asymptotic formula
Borel measure
degenerate differential operator
diffusion equation
Markov semigroup
positive approximation process
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Summary: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.
ISSN:2457-6794
2501-059X
DOI:10.33993/jnaat361-852