Sturm-Liouville operators with matrix distributional coefficients

TL;DR

This paper studies singular Sturm-Liouville operators with matrix distributional coefficients, defining them via regularization, and characterizes their extensions and resolvent convergence in a comprehensive mathematical framework.

Contribution

It introduces a regularization approach for matrix distributional coefficients and describes all self-adjoint and dissipative extensions through boundary conditions.

Findings

Operators are correctly defined as quasi-differentials.

Resolvant convergence of the operators is established.

All extensions are characterized by boundary conditions.

Abstract

The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent convergence is investigated and all self-adjoint, maximal dissipative, and maximal accumulative extensions are described in terms of homogeneous boundary conditions of the canonical form.