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.

7 pages, no figures, submitted

References in corpus (2)

• Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin
• A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter