To the Spectral Theory of the Bessel Operator on Finite Interval and Half-Line

TL;DR

This paper investigates the spectral properties and self-adjoint extensions of the Bessel operator on finite intervals and half-lines, providing a comprehensive description of its extensions and the Friedrichs extension using advanced operator theory techniques.

Contribution

It offers a complete characterization of all non-negative self-adjoint extensions of the Bessel operator and describes the Friedrichs extension's domain via boundary triplets and quadratic forms.

Findings

All non-negative self-adjoint extensions are explicitly described.

The domain of the Friedrichs extension is characterized using boundary triplets.

The approach combines extension theory, boundary triplets, and quadratic forms.

Abstract

The minimal and maximal operators generated by the Bessel differential expression on the finite interval and a half-line are studied. All non-negative self-adjoint extensions of the minimal operator are described. Also we obtain a description of the domain of the Friedrichs extension of the minimal operator in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl functions, and by using the quadratic form method.