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.
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页码：229 / 236
页数：8
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