abstract We give a formula for the duals of the mask associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

Non-orthogonal spline wavelets are developed for Galerkin BEM. The proposed wavelets have compact supports and closed-form expressions. Besides of it, one can choose arbitrarily the order of vanishing moments of the wavelets independently of order of B-splines. Sparse coefficient matrices are obtained by truncating the small elements a priori. The memory requirement and computational time can b...

We build wavelet-like functions based on a parametrized family of pseudo-differential operators L~ν that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green function of L~ν , generate a family of L-spline spaces. These spaces have the approximation order equal to the order of the underlying operator. A sequenc...

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...

In wavelet representations, the magnitude of the wavelet coeecients depends on both the smoothness of the represented function f and on the wavelet. We investigate the extreme values of wavelet coeecients for the standard function spaces A k = ff j kf (k) k 2 1g, k 2 N. In particular, we compare two important families of wavelets in this respect, the orthonormal Daubechies wavelets and the semi...

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute refinement mask of B-splines any order in case general scaling factor. Our is solely derived from reproduction properties satisfied by splines it does not require explicit construction or evaluation basis functions. The second part discusses factorization B-spline masks terms a...

This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...

In this paper, We use the wavelet bases of Hermite cubic splines to solve the second kind integral equations xCi) -11 K(t,s)x(s)ds = y(t), t E [0,1]. A pair of wavelets are constructed on the basis of Hermite cubic spline~: This wavelets are in C1 and supported on [0,2]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. This spline wavelets are then adapted to the interval [0...

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...