Reduction of singular integral operators with flip and their fredholm property

被引：9

作者：

Castro L.P. ^{[1
]}

Rojas E.M. ^{[1
]}

机构：

[1] Research Unit Mathematics and Applications, Department of Mathematics, University of Aveiro

来源：

Lobachevskii Journal of Mathematics | 2008年 / 29卷 / 3期

关键词：

Carleman shift; Fredholm property; Hankel operator; Singular integral operator; Toeplitz operator;

D O I：

10.1134/S1995080208030025

中图分类号：

学科分类号：

摘要：

This paper deals with singular integral operators with a reverting orientation Carleman shift defined on the classic Lebesgue space and having essentially bounded functions as coefficients. We will use similarity relations to show that the mentioned operators are equivalent tomatrix Toeplitz plus Hankel operators acting on the corresponding Hardy space. The main purpose is to extract Fredholm characteristics of the initial operators (in the form of necessary and sufficient conditions). Namely, Fredholm criteria are obtained for some of the operators under study when they have coefficients in the classes of continuous, piecewise continuous, and semi-almost-periodic functions. In addition, Fredholm index formulas are also provided in some of these cases. © 2008 MAIK Nauka.

引用

页码：119 / 129

页数：10

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