Multi-interval Sturm-Liouville boundary-value problems with distributional potentials

TL;DR

This paper investigates multi-interval Sturm-Liouville problems with distributional potentials, providing a comprehensive description of their self-adjoint and dissipative extensions using boundary triplet theory.

Contribution

It introduces a framework for analyzing boundary-value problems with distributional potentials, characterizing all extensions via boundary conditions.

Findings

All real maximal dissipative and accumulative extensions are self-adjoint.

Constructive descriptions of all extensions and resolvents are provided.

Boundary triplet methods are applied to multi-interval Sturm-Liouville problems.

Abstract

We study the multi-interval boundary-value Sturm-Liouville problems with distributional potentials. For the corresponding symmetric operators boundary triplets are found and the constructive descriptions of all self-adjoint, maximal dissipative and maximal accumulative extensions and generalized resolvents in terms of homogeneous boundary conditions are given. It is shown that all real maximal dissipative and maximal accumulative extensions are self-adjoint and all such extensions are described.