Iterates of Markov Operators and Constructive Approximation of Semigroups

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Constructive Mathematical Analysis
Volume:2 Issue:1
Iterates of Markov Operators and Constructive Approximation of Semigroups

Iterates of Markov Operators and Constructive Approximation of Semigroups

Pages : 22-39

View : 45 | Download : 8

Publication Date : 2019-03-01

Article Type : Research Paper

Abstract :In this paper we survey some recent results concerning the asymptotic behaviour of the iterates of a single Markov operator or of a sequence of Markov operators. Among other things, a characterization of the convergence of the iterates of Markov operators toward a given Markov projection is discussed in terms of the involved interpolation sets. Constructive approximation problems for strongly continuous semigroups of operators in terms of iterates are also discussed. In particular we present some simple criteria concerning their asymptotic behaviour. Finally, some applications are shown concerning Bernstein-Schnabl operators on convex compact sets and Bernstein-Durrmeyer operators with Jacobi weights on the unit hypercube. A final section contains some suggestions for possible further researches.
Keywords : Markov operator, Iterate of Markov operators, Markov semigroup, Approximation of semigroups, Bernstein Schnabl operator, Bernstein Durrmeyer operator with Jacobi weights

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