Operator identities corresponding to inverse problems

Abstract

The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that operators with the close to displacement kernels are included in this class. A special case of positive and factorizable operators is dealt with separately.

References in corpus (2)

• Construction of the solution of the inverse spectral problem for a system depending rationally on the spectral parameter, Borg-Marchenko-type theorem, and sine-Gordon equation
• Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular matrix potential

Cited by in corpus (1)

• Inversion of the convolution operators on a rectangular