Multipoint Normal Differential Operators of Second Order

TL;DR

This paper characterizes all normal extensions of a second-order multipoint differential operator in a Hilbert space, providing a detailed description of their boundary conditions and analyzing the spectral structure of these extensions.

Contribution

It offers a complete description of normal extensions for multipoint second-order differential operators and investigates their spectral properties.

Findings

All normal extensions are described via boundary conditions at endpoints.

The spectral structure of these extensions is thoroughly analyzed.

The work advances understanding of multipoint differential operators in Hilbert spaces.

Abstract

In this work it is described all normal extensions of a multipoint minimal operator generated by linear multipoint differential-operator expression for second order in the Hilbert space of vector-functions in terms of boundary values at the endpoints of the infnitely many subintervals. Finally, a spectrum structure of such extensions has been investigated.