On a Poisson summation formula for noncommutative tori
Igor Nikolaev
TL;DR
This paper establishes a Poisson summation formula for noncommutative tori by showing a maximal abelian subalgebra commutes with the Laplace operator, bridging classical and noncommutative harmonic analysis.
Contribution
It introduces an analog of the Poisson summation formula for noncommutative tori based on the commutation properties of a maximal abelian subalgebra.
Findings
Maximal abelian subalgebra commutes with Laplace operator
Derived an analog of Poisson summation formula for noncommutative tori
Bridged classical harmonic analysis with noncommutative geometry
Abstract
It is proved that a maximal abelian subalgebra of the noncommutative torus commutes with the Laplace operator on a complex torus. As a corollary, one gets an analog of the Poisson summation formula for noncommutative tori.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Geometric and Algebraic Topology