Generalized indefinite strings with purely discrete spectrum

TL;DR

This paper develops criteria for when the spectrum of generalized indefinite strings is purely discrete and satisfies Schatten-von Neumann properties, with applications to the Camassa-Holm flow and Schrödinger operators with delta-prime interactions.

Contribution

It introduces new spectral criteria for generalized indefinite strings and applies these to specific physical and mathematical models.

Findings

Criteria for purely discrete spectrum established

Schatten-von Neumann properties characterized

Applications to Camassa-Holm flow and delta'-interactions

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 Schr\"odinger operators with $\delta'$-interactions.