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2011

Convolution and involution on function spaces of homogeneous spaces

Farashahi, Arash Ghaani

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Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$.

It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space $L^1(G/H,\mu)$ 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 $G/H$.

Convolution and involution on function spaces of homogeneous spaces · Around

Built on

Hewitt. E. and Ross. K. A., Absrtact Harmonic Analysis
1963
Earlier work this paper cites.
Folland. G. B., A Course in Abstract Harmonic Analysis
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Earlier work this paper cites.
Forrest. B., Fourier analysis on coset spaces
1998
Earlier work this paper cites.

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Then

Kamyabi-Gol. R. A. and Tavallaei. N., Convolution and homogeneous spaces
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