Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions

Publication date: 22 June 2023

Abstract: We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions are treated as well. Moreover, we present necessary and sufficient conditions on the given distribution matrix valued function to be a spectral function of some Dirac system with a locally square-integrable potential. Interesting connections with Paley-Wiener sampling measures appear in the case of scalar spectral functions.

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Inverse problems involving ordinary differential equations (34A55)

This page was built for publication: Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6441134)