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

Raven Waller

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

General Topology 2019-02-11 v1 Group Theory

Authors: Raven Waller

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.

Keywords

harmonic analysis non-locally compact groups level structures locally compact groups compactness generalization topological results tychonoff theorem

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@article{arxiv.1902.02909,
  title  = {An approach to harmonic analysis on non-locally compact groups I: level structures over locally compact groups},
  author = {Raven Waller},
  journal= {arXiv preprint arXiv:1902.02909},
  year   = {2019}
}

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30 pages

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

Abstract

Keywords

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