Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

In the past decade research on the multiresolution analysis has made considerable progress due to its wide applications. For the basic theory of multiresolution we refer readers to the work in 1, 2 . Recently, we find that a lot of authors try to extend the theory of wavelets on the Euclidean space to nilpotent Lie groups see 3–6 . In this paper we will give the definition of acceptable dilatio...

Haar wavelets and multiresolution analysis

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

Haar Wavelets on Spherical Triangulations

We construct piecewise constant wavelets on spherical triangulations, which are orthogonal with respect to a scalar product on L(S), defined in [3]. Our classes of wavelets include the wavelets obtained by Bonneau in [1] and by Nielson et all. in [2]. We also proved the Riesz stability and showed some numerical experiments.

Wavelets with Frame Multiresolution Analysis

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...