Approximation properties of multivariate wavelets
Mathematics of Computation
Multivariate refinement equations and convergence of subdivision schemes
SIAM Journal on Mathematical Analysis
Computing the Smoothness Exponent of a Symmetric Multivariate Refinable Function
SIAM Journal on Matrix Analysis and Applications
Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
Vector cascade algorithms and refinable function vectors in Sobolev spaces
Journal of Approximation Theory
Hi-index | 0.00 |
We study multivariate trigonometric polynomials satisfying the "sum-rule" conditions of a certain order. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest in the analysis of convergence and smoothness of multivariate subdivision schemes associated with general dilation matrices. The approach presented in this paper leads directly to constructive algorithms, and is an alternative to the analysis of multivariate subdivision schemes in terms of the joint spectral radius of certain operators. Our convergence results apply to arbitrary dilation matrices, while the smoothness results are limited to two classes of dilation matrices.