Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some -algebras of pseudo-differential operators with coefficients which either have limits at , 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. All computations are explicitly performed.
Cite this article
Hideki Inoue, Serge Richard, Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1359–1380DOI 10.4171/JNCG/349