Spectral identities for Schrödinger operators

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 G...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 68; no. 2; pp. 484 - 491
Main Author Guliyev, Namig J.
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.06.2025
Subjects
34L40
Spectral identities
one-dimensional Schrödinger equation
boundary conditions dependent on the eigenvalue parameter
34A55
34L15
15B05
Sturm–Liouville operator
34B07
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Summary: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.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439524000407