부산대학교 도서관

The Chébli-Trimèche hypergroups are a family of hypergroup structures on $[0,\infty)$ that include the ones associated to Bessel and Jacobi functions. This paper is concerned with hypergroups $X$ that are the product of a Chébli-Trimèche hypergroup and the group ${\bold R}^n$. After a review of the elements of harmonic analysis on $X$, the authors define generalized wavelets on $X$ and use them to define continuous wavelet transforms on $X$. They prove the Plancherel and inversion theorems for these transforms and give a characterization of their ranges.