Multiresolution analysis and Haar wavelets on the Laguerre hypergroup (Q1036514)

Summary: Let \(\mathbb H^{n}\) be the Heisenberg group. The fundamental manifold of the radial function space for \(\mathbb H^{n}\) can be denoted by \([0,+\infty )\times \mathbb R\), which is just the Laguerre hypergroup. In this paper the multiresolution analysis on the Laguerre hypergroup \(\mathbb K=[0,+\infty )\times \mathbb R\) is defined. Moreover the properties of Haar wavelet bases for \(L_a^{2}(\mathbb K)\) are investigated.