Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups
Printed: Mar 2017
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
Then, we present a generalized abstract notion of Plancherel
(trace) formula for the Hilbert space $L^2(G/H,\mu)$.
compact group, homogeneous space, dual space, Plancherel (trace) formula
20G05 - Representation theory
43A85 - Analysis on homogeneous spaces
43A32 - Other transforms and operators of Fourier type
43A40 - Character groups and dual objects