This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

We present a new kind of second generation wavelets on a rectangular grid. These wavelets are constructed using a 2D lifting scheme which is based on a red-black blocking scheme. Compared to classical tensor product wavelets on the same grid, these new wavelets show less anisotropy. The performance of the new wavelets is compared to tensor product wavelets in an image denoising application.

Our concern is with the construction of a frame in L 2 (S) consisting of smooth functions based on kernels of spherical harmonics. The corresponding decomposition and reconstruction algorithms utilize discrete spherical Fourier transforms. Numerical examples connrm the theoretical expectations. x1. Introduction Traditionally, wavelets were tailored to problems on the Euclidean space IR d. Howev...

Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...

We prove three results on wavelets for the Hardy space H (R). All wavelets constructed so far for H(R) are MSF wavelets. We construct a family of H-wavelets which are not MSF. An equivalence relation on H-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H-wavelets with Fourier transform discontinuous at the origin.

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang [2]. A cha...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provi...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provided.

We introduce ternary wavelets, based on an interpolating 4-point C ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). H...