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

摘要

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.