Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions
Spectral Theory
2026-04-29 v1 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
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.
Cite
@article{arxiv.2306.12976,
title = {Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:2306.12976},
year = {2026}
}
Comments
This work is an important development of our earlier papers arXiv:1401.3605 and arXiv:1611.00550