Spectral asymptotics for the fourth-order operator with periodic coefficients

TL;DR

This paper investigates the spectral properties of a self-adjoint fourth-order differential operator with periodic coefficients, deriving the asymptotic behavior of its eigenvalues at high energy levels.

Contribution

It provides the first detailed high energy asymptotic analysis of eigenvalues for this class of fourth-order periodic operators.

Findings

Eigenvalues exhibit specific asymptotic behavior at high energies

Spectrum is discrete and well-characterized asymptotically

Results extend understanding of spectral theory for higher-order operators

Abstract

We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.