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.
