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 $\hat{I}{´}^{\prime }$-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