Selfadjoint and $m$ sectorial extensions of Sturm-Liouville operators

TL;DR

This paper characterizes self-adjoint and m-sectorial extensions of coercive Sturm-Liouville operators under minimal smoothness assumptions on the coefficients, advancing the understanding of their spectral properties.

Contribution

It provides a comprehensive characterization of these extensions with minimal smoothness conditions, filling gaps in the spectral theory of Sturm-Liouville operators.

Findings

Characterization of self-adjoint extensions

Characterization of m-sectorial extensions

Minimal smoothness conditions sufficing for the theory

Abstract

The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.