Classical harmonic analysis over spaces of complex measures on coset spaces of compact subgroups

Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

“…First, we review some results concerning classical aspect of the function space C 0 (G/H). These classical aspects concerning the fucntion space C 0 (G/H) studied for the case G is comapct in [15] and extended for the case G is locally comapct and H is compact in [11].…”

“…Throughout this section, we review some of basic results concerning abstract harmonic analysis over spaces of complex measures on coset spaces of compact subgroups in locally compact groups, for details and proofs see [11,15]. Also, it is still assumed that G is a locally compact group, H is a compact subgroup of G, and µ is the normalized G-invariant measure over the left coset space G/H associated to (2.9) with respect to the fixed left Haar measure dx = dσ(x) of G and the probability measure of H. It should be mentioned that, from now on by a complex measure we mean a regular countably additive complex Borel measure.…”

“…The following results studied for the case G is compact in [15] and extended for the case G is locally comapct and H is compact in [11].…”