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