Vol. 94, No. 1, 1981

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Spectral synthesis in products and quotients of hypergroups

Ajay Kumar and Ajit Kaur Chilana

Vol. 94 (1981), No. 1, 177–192

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.

Mathematical Subject Classification 2000
Primary: 43A45
Secondary: 22A10
Received: 4 May 1979
Revised: 5 December 1979
Published: 1 May 1981
Ajay Kumar
Ajit Kaur Chilana