Spectral identities for Schrödinger operators

Abstract

We obtain a system of identities relating boundary coefficients and spectral data for the one-dimensional Schrödinger 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.

arXiv comment7 pages, no figures, submitted

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