Vol. 94, No. 1, 1981

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ISSN: 0030-8730
Spectral synthesis in products and quotients of hypergroups

Ajay Kumar and Ajit Kaur Chilana

Vol. 94 (1981), No. 1, 177–192
Abstract

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
Milestones
Received: 4 May 1979
Revised: 5 December 1979
Published: 1 May 1981
Authors
Ajay Kumar
Ajit Kaur Chilana