FACTORIZATION OF SINGULAR INTEGRAL OPERATORS WITH A CARLEMAN SHIFT AND SPECTRAL PROBLEMS

In this paper we study singular integral operators with a linear fractional Carleman shift preserving the orientation on the unit circle. The main goal is to characterize the spectrum of some of these operators. To this end a special factorization of the operator is derived with the help of a factor...

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Bibliographic Details
Published in:The Journal of integral equations and applications 2001-12, Vol.13 (4), p.339-383
Main Authors: KRAVCHENKO, V.G., LEBRE, A.B., RODRÍGUEZ, J.S.
Format: Article
Language:English
Subjects:
Algebra
Continuous functions
Factorization
Mathematical functions
Mathematical integrals
Matrices
Polynomials
Rational functions
Subalgebras
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Summary:In this paper we study singular integral operators with a linear fractional Carleman shift preserving the orientation on the unit circle. The main goal is to characterize the spectrum of some of these operators. To this end a special factorization of the operator is derived with the help of a factorization of a matrix function in a suitable algebra. After developing methods which permit us to obtain a factorization of a matrix function for some classes of interest, the spectral analysis of some types of singular integral operators with a Carleman shift is done.
ISSN:0897-3962
1938-2626
DOI:10.1216/jiea/1020254809