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Calculation of the Defect Numbers of the Generalized Hilbert and Carleman Boundary Value Problems with Linear Fractional Carleman Shift

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Abstract.

The defect numbers of the generalized Hilbert and Carleman boundary value problems with a direct or an inverse linear fractional Carleman shift of order 2 (α (α (t)) ≡ t) on the unit circle are computed. The approach followed consists of the reduction of the mentioned problems to singular integral equations with linear fractional Carleman shift and of the factorization of Hermitian matrix functions with negative determinant.

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Authors and Affiliations

  1. Departamento de Matemática e Engenharias, Universidade da Madeira, Campus Universitário da Penteada, 9000-390, Funchal, Portugal

    Jorge Ferreira, Gueorgui S. Litvinchuk & Maurício D. L. Reis

  2. Marine Hydrophysical Institute - Hydroacoustic Department, Ukrainian Academy of Sciences, Preobrazhenskaya Street 3, 270 100, Odessa, Ukraine

    Gueorgui S. Litvinchuk

Authors
  1. Jorge Ferreira
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  2. Gueorgui S. Litvinchuk
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  3. Maurício D. L. Reis
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Correspondence to Maurício D. L. Reis.

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Ferreira, J., Litvinchuk, G.S. & Reis, M.D.L. Calculation of the Defect Numbers of the Generalized Hilbert and Carleman Boundary Value Problems with Linear Fractional Carleman Shift. Integr. equ. oper. theory 57, 185–207 (2007). https://doi.org/10.1007/s00020-006-1451-3

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  • DOI: https://doi.org/10.1007/s00020-006-1451-3

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