On the Fourier transformation of positive, positive definite measures on commutative hypergroups, and dual convolution structures (Q1176272)

The author investigates the support of the Fourier transform of a shift- bounded positive, positive-definite measure on a commutative hypergroup \(K\). The main result shows the existence of a positive character contained in the support of the Fourier transform of such a measure. This result extends the known fact that the support of the Plancherel measure contains a positive character, a result shown by the author in a previous paper [Math. Z. 198, 405-421 (1988; Zbl 0677.43002)]. In a second section the author applies this result to the dual convolution structure on \(\hat K\) or on subsets of \(\hat K\) whenever such a dual convolution exists. Various classes of examples are studied.