An Estimate for the Dimension of the Kernel of a Singular Operator with a Non-Carleman Shift

Viktor G. Kravchenko () and Rui C. Marreiros ()
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Viktor G. Kravchenko: Universidade do Algarve, Área Departamental de Matemática, F.C.T.
Rui C. Marreiros: Universidade do Algarve, Área Departamental de Matemática, F.C.T.

A chapter in Factorization, Singular Operators and Related Problems, 2003, pp 197-204 from Springer

Abstract: Abstract An estimate for the dimension of the kernel of the singular integral operator I−cUP +, L 2 n (T) → L 2 n (T), with a non-Carleinan shift is obtained, where P + is the Cauchy projector, U is the isometric shift operator and c(t) is a continuous matrix function. It is supposed that the shift has a finite set of fixed points and all the eigenvalues of the matrix c(t) at the fixed points, simultaneously belong either to the interior of the unit circle T or to its exterior.

Keywords: singular integral operators; shift operators. (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0227-0_13

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DOI: 10.1007/978-94-017-0227-0_13

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