Vol. 85, No. 1, 1979

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Harmonic analysis on compact hypergroups

Richard Vrem

Vol. 85 (1979), No. 1, 239–251

Let K be a compact hypergroup (convo) as defined by R. Jewett. It is shown that Trig (K) is uniformly dense in C(K) and the Peter-Weyl theorem holds. A generalization of the Weil character formula is obtained and a Fourier transform is defined. Analogues of the Riemann-Lebesgue lemma, Parseval’s identity and the Riesz-Fischer theorem are proved in this setting. The space A(K) of functions in L1(K) with absolutey convergent Fourier series is shown to be the linear span of the positive-definite functions on K and the equality A(K) = L2(K) L2(K) is established.

Mathematical Subject Classification 2000
Primary: 43A30
Secondary: 43A10
Received: 19 November 1977
Published: 1 November 1979
Richard Vrem