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*--dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus C∞(Tn), as Rieffel deformations of the standard pseudodifferential operators on C∞(Tn), and in association to certain spectral triples.
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