Algebra of singular integral operators with a Carleman backward slowly oscillating shift |
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Authors: | Yu I Karlovich A B Lebre |
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Institution: | (1) Departamento de Matemáticas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 México, D.F., México;(2) Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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Abstract: | In this paper we study the Banach algebra of singular integral operators with piecewise continuous coefficients and a Carleman orientation-reversing slowly oscillating shift on the Lebesgue space with a power weight on the unit circle. The slow oscillation of the shift derivative, in contrast to the classic assumption on its piecewise continuity, leads to the appearance of massive local spectra for the considered operators. Applying localization techniques and the theory of Mellin pseudodifferential and associated limit operators, we construct a symbol calculus for the above-mentioned operator algebra and find a Fredholm criterion and an index formula for the operators in this algebra in terms of their symbols.Partially supported by CONaCYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México.Partially supported by F. C. T. grant Praxis XXI/2/2.1/MAT/441/94, Portugal. |
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Keywords: | MSC 1991" target="_blank">MSC 1991 Primary 47G10 47D30 47A53 Secondary 47G30 45E05 45E10 |
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