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

Farashahi, Arash Ghaani

Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 111-121

Résumé

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 ${{L}^{2}}\left( {G}/{H,\,\mu }\; \right)$ .

Détail

DOI : 10.4153/CMB-2016-037-6

Mots-clés : 20G05, 43A85, 43A32, 43A40, compact group, homogeneous space, dual space, Plancherel (trace) formula

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