Resolvent convergence of Sturm-Liouville operators with singular potentials

TL;DR

This paper establishes conditions under which Sturm-Liouville operators with singular complex potentials can be approximated in the norm resolvent sense, advancing understanding of their spectral properties.

Contribution

It provides new sufficient conditions for the resolvent convergence of Sturm-Liouville operators with singular potentials in Hilbert spaces.

Findings

Sufficient conditions for norm resolvent approximation

Extension to operators with complex singular potentials

Improved understanding of spectral convergence

Abstract

In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent approximation by the operators of the same class.