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

In: Factorization, Singular Operators and Related Problems

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Viktor G. Kravchenko & Rui C. Marreiros, 2003. "An Estimate for the Dimension of the Kernel of a Singular Operator with a Non-Carleman Shift," Springer Books, in: Stefan Samko & Amarino Lebre & António F. dos Santos (ed.), Factorization, Singular Operators and Related Problems, pages 197-204, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0227-0_13
    DOI: 10.1007/978-94-017-0227-0_13
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