Product formulas and convolutions for the radial oblate spheroidal wave functions (Q1582339)

Here the authors obtain a product formula for the oblate radial spheroidal wave functions. The product formula is given for all \((\alpha, \nu)\) with \(\alpha\geq -1/2\) and \(\nu\geq 0\). This product formula is then used to define a convolution of measures, and the resulting measure algebras are described. These measures are positive for \(-1/2\leq \alpha\leq 1/2\), \(\mu\geq 0\). Some of these are new hypergroups. It is further shown that a number of historically important non-compact hypergroups can be thought of as special cases of the measure algebras that arise with oblate spheroidal wave functions as characters.