A Wiener–Tauberian and a Pompeiu type theorems on the Laguerre hypergroup

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• 作者：M.M. Nessibi ; B. Selmi
• 关键词：Wiener– ; Tauberian theorem ; Pompeiu problem ; Hypergroups ; Laguerre hypergroup ; Convolution ; Translation operators ; Fourier transform
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2009
• 出版时间：1 March 2009
• 年：2009
• 卷：351
• 期：1
• 页码：232-243
• 全文大小：281 K

文摘

A Wiener–Tauberian theorem is proven on the Laguerre hypergroup [M.M. Nessibi, K. Trimèche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 337–363]. As consequence of this theorem we establish a Pompeiu type-theorem and we study some of its applications.