Abstract harmonic analysis on locally compact right topological groups
Prachi Loliencar

TL;DR
This paper extends the theory of Haar measures and analytic properties to locally compact right topological groups, providing new conditions for their existence and generalizing classical results beyond the compact admissible case.
Contribution
It introduces sufficient conditions for Haar measure existence on locally compact right topological groups and generalizes analytic theory to this broader setting.
Findings
Established new criteria for Haar measure existence
Generalized analytic properties to non-compact right topological groups
Characterized Haar measure existence without admissibility constraints
Abstract
Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this paper, we broaden the scope of this work. We give (similar) sufficient conditions for the existence of a Haar measure on locally compact right topological groups and generalize analytic theory to this setting. We then define new measure algebra analogues in the compact setting and use these to completely characterize the existence of a Haar measure, producing sufficient conditions that do not rely on admissibility.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering
