Factorization of singular integral operators with a Carleman backward shift: The case of bounded measurable coefficients |
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Authors: | V G Kravchenko A B Lebre J S Rodríguez |
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Institution: | (1) Departamento De Matemática, F.C.T. Universidade Do Algarve, Campus De Gambelas, 8000-810 Faro, Portugal;(2) Departamento De Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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Abstract: | In this paper, we generalize our recent results concerning scalar singular integral operators with a Carleman backward shift,
allowing more general coefficients, bounded measurable functions on the unit circle. Our aim is to obtain an operator factorization
for singular integral operators with a backward shift and bounded measurable coefficients, from which such Fredholm characteristics
as the kernel and the cokernel can be described. The main tool is the factorization of matrix functions. In the course of
the analysis performed, we obtain several useful representations, which allow us to characterize completely the set of invertible
operators in that class, thus providing explicit examples of such operators
Dedicated to Professor A. Ferreira dos Santos on the occasion of his seventieth birthday |
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