Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum

Abstract

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\phi (H)-\phi (H_0)$ for piecewise continuous functions $\phi$. This description involves the scattering matrix for the pair $H$, $H_0$.

Latex, 25 pages