Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces

DOI10.1090/S0002-9947-99-02185-6zbMath1052.42029MaRDI QIDQ4257575

Rong-Qing Jia

Publication date: 31 August 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

waveletsregularitySobolev spacessmoothnessapproximation orderLipschitz spacesrefinable functionstransition operatorssubdivision operatorsrefinement equations

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functional equations and inequalities (39B99)

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Cites Work

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• Using the refinement equation for the construction of pre-wavelets. V: Extensibility of trigonometric polynomials
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• Sobolev Characterization of Solutions of Dilation Equations
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• On linear independence for integer translates of a finite number of functions
• Wavelet Analysis of Refinement Equations
• Smooth Refinable Functions Provide Good Approximation Orders
• Stability and Orthonormality of Multivariate Refinable Functions
• Multidimensional Interpolatory Subdivision Schemes
• Approximation properties of multivariate wavelets
• The Toeplitz Theorem and its Applications to Approximation Theory and Linear PDE's
• Stability of Refinable Functions, Multiresolution Analysis, and Haar Bases

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