Faculté des Sciences de Bizerte, Département de Mathématiques, 7021 Zarzouna, Tunisia
Abstract:
We consider here the Laguerre hypergroup (K,α*), where K=0,+∞×R and α* a convolution product on K coming from the product formula satisfied by the Laguerre functions (m∈N, α?0). We set on this hypergroup a local central limit theorem which consists to give a weakly estimate of the asymptotic behavior of the convolution powers μα*k=μα*?α*μ (k times), μ being a given probability measure satisfying some regularity conditions on this hypergroup. It is also given a central local limit theorem for some particular radial probability measures on the (2n+1)-dimensional Heisenberg group Hn.