Asymptotic behavior of the integrated density of states of acoustic operators with random long range perturbations
The study of the integrated density of states and specially of its behaviour is of interest for its relationship with physical interpretations. The question the author is interested in the paper deals with the behaviour of the integrated density of states at the internal spectral edges of \(A_\omega=- \sum^d_{i=1} \partial_{x_i}{1\over\rho_\omega} \partial_{x_i}\), where \(\rho_\omega\) is a positive and bounded function which represents the mass density or the elasticity contrast of the medium where the wave propagates. Here \(A_\omega\) is a selfadjoint operator on \(L^2(\mathbb{R}^d)\).
scientific article; zbMATH DE number 2085877