Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 975901, 8 pages
doi:10.1155/2009/975901
Research Article

Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

Peizhu Xie and Jianxun He

Department of Mathematics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Received 26 September 2008; Accepted 7 April 2009

Academic Editor: Alexander P. Seyranian

Copyright © 2009 Peizhu Xie and Jianxun He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let ℍn be the Heisenberg group. The fundamental manifold of the radial function space for ℍn can be denoted by [0,+∞)×ℝ, which is just the Laguerre hypergroup. In this paper the multiresolution analysis on the Laguerre hypergroup 𝕂=[0,+∞)×ℝ is defined. Moreover the properties of Haar wavelet bases for La2(𝕂) are investigated.