Spectral functions of the simplest even order ordinary differential operator

TL;DR

This paper explicitly determines the spectral functions of the simplest even order differential operator using boundary triplet techniques, providing detailed spectral analysis for its Friedrichs and Krein extensions.

Contribution

It introduces explicit formulas for the spectral functions of a fundamental even order differential operator via boundary triplet and Weyl function methods.

Findings

Explicit spectral functions for Friedrichs and Krein extensions

Characteristic matrix derived for the operator

Spectral analysis using boundary triplet techniques

Abstract

We consider the minimal differential operator A generated in $L^2(0,\infty)$ by the differential expression $l(y) = (-1)^n y^{(2n)}$. Using the technique of boundary triplets and the corresponding Weyl functions, we find explicit form of the characteristic matrix and the corresponding spectral function for the Friedrichs and Krein extensions of the operator A.