On Generalized Strong and Norm Resolvent Convergence

TL;DR

This paper introduces a streamlined method for analyzing the convergence of self-adjoint operators in different Hilbert spaces, focusing on their spectral properties and applications to Sturm-Liouville problems.

Contribution

It provides a new approach to generalized strong and norm resolvent convergence, including convergence of associated semigroups, spectra, and spectral projections, with applications to Sturm-Liouville operators.

Findings

Established convergence of (semi-)groups and spectra

Proved convergence of spectral projections

Applied results to Sturm-Liouville operators

Abstract

We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral projections. In addition, we give some applications to Sturm-Liouville operators.