On the common Point Spectrum of pairs of Self-Adjoint Extensions

TL;DR

This paper investigates the intersection of point spectra of two different self-adjoint extensions of the same symmetric operator, providing insights and examples to understand their spectral relationships.

Contribution

It offers a new analysis of the common point spectrum of pairs of self-adjoint extensions, with illustrative examples.

Findings

Identifies conditions for shared eigenvalues.

Provides explicit examples of spectral intersections.

Enhances understanding of spectral properties of extensions.

Abstract

Given two different self-adjoint extensions of the same symmetric operator, we analyse the intersection of their point spectra. Some simple examples are provided.