Formally self-adjoint quasi-differential operators and boundary value problems

TL;DR

This paper develops a boundary triplet framework for self-adjoint quasi-differential operators of arbitrary order, enabling comprehensive description of their extensions and resolvents in boundary value problems.

Contribution

It introduces a boundary triplet approach for high-order quasi-differential operators, expanding the analysis of their extensions and resolvents.

Findings

Characterization of all self-adjoint, dissipative, and accumulative extensions

Explicit description of generalized resolvents in boundary terms

Application to specific classes of quasi-differential operators

Abstract

We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal dissipative, accumulative and self-adjoint extensions of the associated minimal operator and its generalized resolvents in terms of the boundary conditions. Some specific classes are considered in greater detail.