Hypoelliptic Jacobi Convolution Operators on Schwartz Distributions

In this paper we characterize the hypoellipticity of Jacobi convolution operators on Schwartz distributions. In the proof of the main result of this paper the positivity ofthe convolution structure for the inverse of the Jacobi transform plays an essential role. We also study hypoelliptic convolution equations on Chébli-Triméche hypergroups.Mathematics Subject Classification 2000: 46F12