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

Published:2016-07-14
Printed: Mar 2017
• Arash Ghaani Farashahi,
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1 A-1090 Wien, Vienna, Austria
 Format: LaTeX MathJax PDF

## Abstract

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 $H$ be a closed subgroup of $G$. Let $G/H$ be the left coset space of $H$ in $G$ and $\mu$ be the normalized $G$-invariant measure on $G/H$ associated to the Weil's formula. Then, we present a generalized abstract notion of Plancherel (trace) formula for the Hilbert space $L^2(G/H,\mu)$.
 Keywords: compact group, homogeneous space, dual space, Plancherel (trace) formula
 MSC Classifications: 20G05 - Representation theory 43A85 - Analysis on homogeneous spaces 43A32 - Other transforms and operators of Fourier type 43A40 - Character groups and dual objects

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