Index theorems for Fredholm, semi-Fredholm and almost-periodic operators; all in one example

Serge Richard, University of Nagoya, Japan

Abstract

Based on operators borrowed from scattering theory, several concrete realizations of index theorems will be presented. The corresponding operators belong to some C*algebras of pseudo-differential operators with coefficients which either have limits at + or - infinity, or which are periodic or asymptotically periodic, or which are uniformly almost periodic. These various situations can be deduced from a single partial isometry which depends on several parameters. From a different point of view, these investigations correspond to a Levinson’s type theorem when an infinite number of bound states is involved.