Point mass perturbations of spectral measures

TL;DR

This paper investigates how adding point masses affects spectral measures of certain operators, using advanced moment problem techniques and extremal properties, with applications to Bessel and Schrödinger operators.

Contribution

It generalizes the moment problem approach to analyze point mass perturbations across a broad class of operators, including specific applications to Bessel and Schrödinger cases.

Findings

Derived general results for spectral measure perturbations

Applied results to Bessel operators

Applied results to generalized Schrödinger operators

Abstract

Using a generalization of the moment problem and the extremal properties of spectral measures corresponding to the selfadjoint extensions of a regular symmetric operator, we study point mass perturbations of spectral measures. We obtain general results for a wide class of operators and apply them to the analysis of point mass perturbations of spectral measures pertaining to Bessel and generalized Schr\"odinger operators.