Pseudodifferential Operators on Noncommutative Tori: a Survey

Abstract

This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^{\ast }$--dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus $C^{\infty }({\mathbb{T}}^n)$, as Rieffel deformations of the standard pseudodifferential operators on $C^{\infty }({\mathbb{T}}^n)$, and in association to certain spectral triples.

References in corpus (2)

• Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results
• A Canonical Trace Associated with Certain Spectral Triples