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arXiv · 2303.03584

Pseudodifferential Operators on Noncommutative Tori: a Survey

Carolina Neira Jiménez
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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 $C^\infty(\mathbb{T}^n)$, as Rieffel deformations of the standard pseudodifferential operators on $C^\infty(\mathbb{T}^n)$, and in association to certain spectral triples.

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Carolina Neira Jiménez. 2023-03-07. Pseudodifferential Operators on Noncommutative Tori: a Survey. https://doi.org/10.1007/s44007-024-00122-0

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