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Spectral identities for Schrödinger operators

Published 13 Oct 2019 in math-ph, math.CA, math.FA, math.MP, and math.SP | (1910.05812v1)

Abstract: We obtain a system of identities relating boundary coefficients and spectral data for the one-dimensional Schr\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter. These identities can be thought of as a kind of mini version of the Gelfand--Levitan integral equation for boundary coefficients only.

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