A Paley-Wiener theorem for Harish-Chandra modules
Heiko Gimperlein, Bernhard Kr\"otz, Job J. Kuit, Henrik Schlichtkrull
TL;DR
This paper establishes a Paley-Wiener theorem for Harish-Chandra modules of real reductive groups, providing new insights and a simplified proof of the Helgason conjecture.
Contribution
It formulates and proves a Paley-Wiener theorem specifically for Harish-Chandra modules, advancing the understanding of harmonic analysis on real reductive groups.
Findings
Proves a Paley-Wiener theorem for Harish-Chandra modules
Provides a new proof of the Helgason conjecture
Enhances the theoretical framework of harmonic analysis
Abstract
We formulate and prove a Paley-Wiener theorem for Harish-Chandra modules for a real reductive group. As a corollary we obtain a new and elementary proof of the Helgason conjecture.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality