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Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups

Published online by Cambridge University Press:  20 November 2018

Arash Ghaani Farashahi
Arash Ghaani Farashahi*
Affiliation:
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Oskar- Morgenstern-Platz 1 A-1090 Wien, Vienna, Austria e-mail: arash.ghaani.farashahi@univie.ac.at ghaanifarashahi@hotmail.com e-mail: arash.ghaani.farashahi@univie.ac.at ghaanifarashahi@hotmail.com
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Abstract

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This paper introduces a unified operator theory approach to the abstract Plancherel (trace) formulas over homogeneous spaces of compact groups. Let $G$ be a compact group and let $H$ be a closed subgroup of $G$. Let ${G}/{H}\;$ be the left coset space of $H$ in $G$ and let $\mu$ be the normalized $G$-invariant measure on ${G}/{H}\;$ associated with Weil’s formula. Then we present a generalized abstract notion of Plancherel (trace) formula for the Hilbert space ${{L}^{2}}\left( {G}/{H,\,\mu }\; \right)$.

Keywords

20G0543A8543A3243A40compact grouphomogeneous spacedual spacePlancherel (trace) formula
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 1 , 01 March 2017 , pp. 111 - 121
Copyright
Copyright © Canadian Mathematical Society 2017

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