Generalized indefinite strings with purely discrete spectrum

Abstract

We establish criteria for the spectrum of a generalized indefinite string to be purely discrete and to satisfy Schatten-von Neumann properties. The results can be applied to the isospectral problem associated with the conservative Camassa-Holm flow and to Schrödinger operators with ${\delta }^{\prime }$-interactions.

This version includes an additional appendix that provides explicit two-sided estimates on Schatten-von Neumann norms that are needed in arXiv:2310.06658

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Cited by in corpus (2)

• Trace formulas and inverse spectral theory for generalized indefinite strings
• The conservative Camassa-Holm flow with step-like irregular initial data