Weyl functions of Dirac systems and of their generalizations: integral representation, inverse problem, and discrete interpolation

Abstract

Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral representation of the Weyl function, and results on interpolation of Weyl functions are also derived.

References in corpus (4)

• Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials
• The boundary control approach to the Titchmarsh-Weyl $m-$function
• 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
• Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials

Cited by in corpus (1)

• Initial Value Problems for Integrable Systems on a Semi-Strip