In this paper we first discuss
the coset spaces K∕H and K∕∕H of left cosets and double cosets respectively of a
hypergroup K by a compact subhypergroup H. This development is then
used to obtain some results connecting spectral synthesis for L1(K∕H) to
that for L1(K) when K is commutative. We also indicate that some of the
results for quotient group carry over to K∕H when H is a subgroup of the
center Z(K) of K. Finally we discuss how Malliavin’s theorem fails in a
strong way in many hypergroups and further show that for certain closed sets
of the form E1× E2 in K1×K2, where K1=R+,Z+ etc. and K2 is a
locally compact commutative hypergroup such that the dual K2 of K2 is a
σ-compact hypergroup, E1× E2 can inherit various properties of E1 such as
being nonspectral, non ultra-strong Ditkin for the respective hypergroup
algebras.
