About a result of S.M. Kozlov

TL;DR

This paper provides an alternative proof and enhancements to Kozlov's result concerning the asymptotic behavior of the integrated density of states for a specific acoustic operator at the spectrum's lower end.

Contribution

It introduces a new proof method and improves the existing asymptotic results for the integrated density of states of the acoustic operator.

Findings

New proof of Kozlov's asymptotic result

Improved asymptotic estimates for the integrated density of states

Enhanced understanding of spectral properties of the acoustic operator

Abstract

We give an alternative proof and improve upon a result of S.M. Kozlov \cite{ko}. It deals with the asymptotic of the integrated density of states of the acoustic operator $\displaystyle H_\omega=-\nabla\rho_\omega\nabla$, at the bottom of the spectrum.