Compact Inverses of The Multipoint Normal Diferential Operators For First Order

TL;DR

This paper characterizes all normal extensions of a multipoint first-order differential operator in a Hilbert space and investigates the compactness of their inverses, contributing to the spectral theory of such operators.

Contribution

It provides a complete description of normal extensions of multipoint first-order differential operators and analyzes the compactness of their inverses.

Findings

All normal extensions are explicitly described in terms of boundary conditions.

Conditions for the compactness of the inverses are established.

The results advance understanding of spectral properties of multipoint differential operators.

Abstract

In this work, firstly all normal extensions of a multipoint minimal operator generated by linear multipoint diferential-operator expression for first order in the Hilbert space of vector functions in terms of boundary values at the endpoints of the infinitely many separated subintervals are described. Finally, a compactness properties of the inverses of such extensions has been investigated.