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* C ∗ -dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus C^∞ (Tⁿ) C ∞ ( T n ) , as Rieffel deformations of the standard pseudodifferential operators on C^∞ (Tⁿ) C ∞ ( T n ) , and in association to certain spectral triples.
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Carolina Neira Jiménez (2024) studied this question.
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