Generalized Kantorovich Operators on Bauer Simplices and Their Limit Semigroups. (3rd June 2017)

• Record Type: Journal Article
• Authors: Cappelletti-Montano, Mirella; Leonessa, Vita
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 6(2017)
• Page Start: 723
• Page End: 737
• Publication Date: 2017-06-03
• Subjects: Approximation of semigroup -- Bauer simplex -- Bernstein–Schnabl operator -- Canonical Markov projection -- Kantorovich operator -- Markov semigroup -- Positive approximation process; 41A36 -- 47D07 -- 31A10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1281825
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we prove an asymptotic formula for generalized Kantorovich operators associated with the canonical Markov projection on a given Bauer simplex K . That formula involves an operator acting on the subalgebra of all products of affine functions on K . Moreover, we prove that such an operator is closable and its closure is the generator of a Markov semigroup which, in turn, may be represented in terms of iterates of the above-mentioned generalized Kantorovich operators.