A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups
This paper introduces a class of abstract linear representations
Banach convolution function algebras over
homogeneous spaces of compact groups. Let $G$ be a compact group
and $H$ be a closed subgroup of $G$.
Let $\mu$ be the normalized $G$-invariant measure over the compact
homogeneous space $G/H$ associated to the
Weil's formula and $1\le p\lt \infty$.
We then present a structured class of abstract linear representations
Banach convolution function algebras $L^p(G/H,\mu)$.
homogeneous space, linear representation, continuous unitary representation, convolution function algebra, compact group, convolution, involution
43A85 - Analysis on homogeneous spaces
47A67 - Representation theory
20G05 - Representation theory