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Lobachevskii Journal of Mathematics

, Volume 29, Issue 3, pp 119–129 | Cite as

Reduction of singular integral operators with flip and their Fredholm property

Article

Abstract

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.

Key words and phrases

Singular integral operator Carleman shift Toeplitz operator Hankel operator Fredholm property 

2000 Mathematics Subject Classification

47G10 47B35 47A53 45E05 45F15 47A20 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Research Unit Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal

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