Vol. 76, No. 2, 1978

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Spectral synthesis in hypergroups

Ajit Kaur Chilana and Kenneth Allen Ross

Vol. 76 (1978), No. 2, 313–328

A commutative hypergroup K is, roughly speaking, a space in which the product of two elements is a probability measure. Such spaces have been studied by Dunkl, Jewett, and Spector. Examples include locally compact abelian groups and double-coset spaces. K has a Haar measure m (Spector). It is shown that for several important classes of hypergroups lhe structure space of L1(m) is a hypergroup K. For such spaces, L1(m) is shown to be regular, in fact, super-regular, and to have good approximate units. A Wiener-Tauberian theorem is given. Points in the center of K are shown to be strong Ditkin sets. Examples (due essentially to Reiter and Naimark) show that not all points in K need be spectral sets.

Mathematical Subject Classification 2000
Primary: 43A45
Received: 8 August 1977
Published: 1 June 1978
Ajit Kaur Chilana
Kenneth Allen Ross