Toeplitz算子和Wiener-Hopf分解:介绍

IF 0.3 Q4 MATHEMATICS

Concrete Operators Pub Date : 2017-10-31 DOI:10.1515/conop-2017-0010

M. Câmara

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引用次数: 7

摘要

摘要Wiener-Hopf因子分解在Toeplitz算子理论中占有重要地位。我们在这里考虑上半平面的Hardy空间Hp中的Toeplitz算子，并回顾了如何根据其符号的Wiener-Hopf因子分解来研究它们的Fredholm性质，获得了算子是Fredholm或可逆的充要条件，以及当这些条件存在时它们的逆或单侧逆的公式。将结果应用于L-1中的一类奇异积分方程(ℝ)

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Toeplitz operators and Wiener-Hopf factorisation: an introduction

Abstract Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)

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来源期刊

Concrete Operators MATHEMATICS-

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

22 weeks