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Ghaani Farashahi, Arash
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 on 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 of the Banach convolution function algebras $L^p(G/H,\mu)$.

Keywords:homogeneous space, linear representation, continuous unitary representation, convolution function algebra, compact group, convolution, involution
Categories:43A85, 47A67, 20G05

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