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arXiv · 2306.12976

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

Alexander Sakhnovich
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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.

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Alexander Sakhnovich. 2023-06-22. Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions. https://arxiv.org/abs/2306.12976

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