Accuracy of lattice translates of several multidimensional refinable functions

DOI10.1006/jath.1997.3211zbMath0911.41008OpenAlexW2144471752MaRDI QIDQ1268712

Christopher Heil, Carlos A. Cabrelli, Ursula M. Molter

Publication date: 1 November 1998

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1997.3211

zbMATH Keywords

waveletsshift invariant spaces

Mathematics Subject Classification ID

Functional inequalities, including subadditivity, convexity, etc. (39B62) Rate of convergence, degree of approximation (41A25) Algorithms for approximation of functions (65D15)

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Cites Work

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• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• Continuity of nonseparable quincunx wavelets
• Fractal functions and wavelet expansions based on several scaling functions
• Approximation order provided by refinable function vectors
• Regularity of refinable function vectors
• Matrix refinement equations: existence and uniqueness
• Approximation by translates of refinable functions
• Non-separable bidimensional wavelet bases
• Wavelets in Wandering Subspaces
• Stationary subdivision
• Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
• Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
• Ten Lectures on Wavelets
• Multivariate matrix refinable functions with arbitrary matrix dilation
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Approximation properties of multivariate wavelets
• Approximation by Multiple Refinable Functions
• Construction of Multiscaling Functions with Approximation and Symmetry
• The Exponentials in the Span of the Multiinteger Translates of a Compactly Supported Function; Quasiinterpolation and Approximation Order
• Construction of Orthogonal Wavelets Using Fractal Interpolation Functions