Cohomology of Fuchsian groups and Fourier interpolation
Mathilde Gerbelli-Gauthier, Akshay Venkatesh
TL;DR
This paper presents a new proof of a Fourier interpolation theorem by linking it to the vanishing of first cohomology groups of Fuchsian groups with Weil representation coefficients.
Contribution
It introduces a novel cohomological approach to establish Fourier interpolation, connecting harmonic analysis with group cohomology.
Findings
New proof of Fourier interpolation theorem
Cohomological vanishing result for Fuchsian groups
Link between harmonic analysis and group cohomology
Abstract
We give a new proof of a Fourier interpolation result first proved by Radchenko-Viazovska, deriving it from a vanishing result of the first cohomology of a Fuchsian group with coefficients in the Weil representation.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Topological and Geometric Data Analysis