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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
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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 compact group, homogeneous space, dual space, Plancherel (trace) formula
MSC Classifications: 20G05, 43A85, 43A32, 43A40 show english descriptions Representation theory
Analysis on homogeneous spaces
Other transforms and operators of Fourier type
Character groups and dual objects
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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