Spectral analysis of an even order differential operator

TL;DR

This paper applies the method of similar operators to analyze an even order differential operator with various boundary conditions, deriving eigenvalue asymptotics, spectral estimates, and semigroup behavior.

Contribution

It introduces a novel application of the method of similar operators to spectral analysis of higher-order differential operators with multiple boundary conditions.

Findings

Eigenvalues asymptotics derived for the operator.

Spectral projections and decompositions estimated.

Asymptotic behavior of the associated analytic semigroup established.

Abstract

Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral decompositions and spectral projections. We also establish the asymptotic behavior of the corresponding analytic semigroup of operators.