Approximation properties of multivariate wavelets

Abstract. Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the approximation properties of multivariate refinable functions. We give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask. We connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators. Finally, we demonstrate that a refinable function in W k−1 1 (Rs) provides approximation order k.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Rong-Qing Jia
• Keywords: Approximation Order, Approximation Properties, MOC 1998, Refinable Function