Geodesic
Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups
Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 111-121

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DOI

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 ${{L}^{2}}\left( {G}/{H,\,\mu }\; \right)$ .
DOI : 10.4153/CMB-2016-037-6
Mots-clés : 20G05, 43A85, 43A32, 43A40, compact group, homogeneous space, dual space, Plancherel (trace) formula 
Farashahi, Arash Ghaani. Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups. Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 111-121. doi: 10.4153/CMB-2016-037-6
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     title = {Abstract {Plancherel} {(Trace)} {Formulas} over {Homogeneous} {Spaces} of {Compact} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {111--121},
     year = {2017},
     volume = {60},
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     doi = {10.4153/CMB-2016-037-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-037-6/}
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