Generalized Kantorovich Operators on Bauer Simplices and Their Limit Semigroups

被引：1

作者：

Cappelletti-Montano, Mirella ^{[1
]}

Leonessa, Vita ^{[2
]}

机构：

[1] Univ Bari A Moro, Dipartimento Matemat, Bari, Italy

[2] Univ Basilicata, Dipartimento Matemat Informat & Econ, Viale Ateneo Lucano 10,Campus Macchia Romana, I-85100 Potenza, Italy

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 06期

关键词：

Approximation of semigroup; Bauer simplex; Bernstein-Schnabl operator; Canonical Markov projection; Kantorovich operator; Markov semigroup; Positive approximation process;

D O I：

10.1080/01630563.2017.1281825

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 ane 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.

引用

页码：723 / 737

页数：15

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