Convolution and involution on function spaces of homogeneous spaces

2011/12/31 by Farashahi, Arash Ghaani
#43A15 #43A85 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1201.0297

Abstract

Let G be a locally compact group and also let H be a compact subgroup of G. It is shown that, if μ is a relatively invariant measure on G/H then there is a well-defined convolution on L¹(G/H,μ) such that the Banach space L¹(G/H,μ) becomes a Banach algebra. We also find a generalized definition of this convolution for other L^p-spaces. Finally, we show that various types of involutions can be considered on G/H.

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