Bernstein Polynomials and Operator Theory

被引：14

作者：

Badea, Catalin ^{[1
]}

机构：

[1] Univ Sci & Technol Lille, Dept Math, Lab Paul Painleve, UMR CNRS 8524, F-59655 Villeneuve Dascq, France

来源：

RESULTS IN MATHEMATICS | 2009年 / 53卷 / 3-4期

关键词：

Bounded linear operators; convergence of iterates; spectral theory; Bernstein polynomials;

D O I：

10.1007/s00025-008-0333-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Kelisky and Rivlin have proved that the iterates of the Bernstein operator (of fixed order) converge to L, the operator of linear interpolation at the endpoints of the interval [0, 1]. In this paper we provide a large class of (not necessarily positive) linear bounded operators T on C[0, 1] for which the iterates T(n) converge towards L in the operator norm. The proof uses methods from the spectral theory of linear operators.

引用

页码：229 / 236

页数：8

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