Harmonic Analysis over adelic spaces
Anton Deitmar
TL;DR
This paper develops harmonic analysis for filtered infinite dimensional modules over rings, extending classical Fourier analysis concepts like duality, inversion, and Poisson summation to all dimensions.
Contribution
It introduces a comprehensive harmonic analysis framework for filtered infinite dimensional modules, generalizing classical harmonic analysis to new algebraic structures.
Findings
Established Pontryagin duality for these modules
Derived Fourier inversion and Plancherel formulas
Proved Poisson summation formula in all dimensions
Abstract
Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring. We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation formula for all dimensions.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · advanced mathematical theories · Advanced Algebra and Geometry