Approximation properties of multivariate wavelets
Open Access
- 1 April 1998
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 67 (222) , 647-665
- https://doi.org/10.1090/s0025-5718-98-00925-9
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 1 k − 1 ( R s ) W_{1}^{k-1}(\mathbb {R}^{s}) provides approximation order k k .Keywords
This publication has 16 references indexed in Scilit:
- The Toeplitz Theorem and its Applications to Approximation Theory and Linear PDE'sTransactions of the American Mathematical Society, 1995
- Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )Transactions of the American Mathematical Society, 1994
- A Bernstein-type inequality associated with wavelet decompositionConstructive Approximation, 1993
- A Dual Basis for the Integer Translates of an Exponential Box SplineRocky Mountain Journal of Mathematics, 1993
- On linear independence for integer translates of a finite number of functionsProceedings of the Edinburgh Mathematical Society, 1993
- Compression of Wavelet DecompositionsAmerican Journal of Mathematics, 1992
- Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and FractalsSIAM Journal on Mathematical Analysis, 1992
- Stationary subdivisionMemoirs of the American Mathematical Society, 1991
- The polynomials in the linear span of integer translates of a compactly supported functionConstructive Approximation, 1987
- Approximation Order from Bivariate C 1 -Cubics: A CounterexampleProceedings of the American Mathematical Society, 1983