A local central limit theorem on the Laguerre hypergroup

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:354

Article

Nessibi, M. M.

关键词: Hypergroup;    Laguerre hypergroup;    Heisenberg group;    Laguerre functions;    Bessel functions;    Harmonic analysis;    Convolution;    Fourier transform;    Probability measure;    Local limit theorem;    Levy's continuity theorem;   

DOI  :  10.1016/j.jmaa.2009.01.029

来源: Elsevier

【 摘 要 】

We consider here the Laguerre hypergroup (K, (*alpha),). where K = [0, + infinity[ x R and (*alpha) a convolution product on K coming from the product formula satisfied by the Laguerre functions L-m((alpha)) (m is an element of N, alpha >= 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 mu*(alpha k) = mu (*alpha) ... (*alpha) mu (k times), mu 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 H-n. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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