An approach to harmonic analysis on non-locally compact groups I: level structures over locally compact groups

2019/02/08 by Raven Waller, Waller, Raven
Mathematics · #22A05 #Advanced Mathematical Physics Problems #Algebraic Geometry and Number Theory #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1902.02909

openalex publication_date 2019/02/08 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's Theorem) for such spaces. We also discuss several possible applications of this framework, including the theory of harmonic analysis on non-locally compact groups.

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• An approach to harmonic analysis on non-locally compact groups II: an\n invariant measure on groups of ordered type

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