ELLIPTIC SCALING FUNCTIONS AS COMPACTLY SUPPORTED MULTIVARIATE ANALOGS OF THE B-SPLINES

DOI10.1142/S0219691314500180zbMath1292.41005arXiv1311.1020OpenAlexW2005368048WikidataQ125330045 ScholiaQ125330045MaRDI QIDQ5411718

Victor G. Zakharov

Publication date: 25 April 2014

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1020

zbMATH Keywords

compact supportpolyharmonic splinescardinal B-splineselliptic scaling functionsisotropic dilation matriceshomogeneous elliptic differential operators

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Multidimensional problems (41A63) Spline approximation (41A15)

Related Items (4)

Rotation properties of 2D isotropic dilation matrices ⋮ Reproducing solutions to PDEs by scaling functions ⋮ Bézier and B-spline curves — A study and its application in wavelet decomposition ⋮ Polynomial spaces reproduced by elliptic scaling functions

Cites Work

• Polyharmonic cardinal splines
• The polynomials in the linear span of integer translates of a compactly supported function
• Elementary \(m\)-harmonic cardinal B-splines
• High level \(m\)-harmonic cardinal B-splines
• Approximation error for quasi-interpolators and (multi-)wavelet expansions
• On the construction of multivariate (pre)wavelets
• Wavelet-Galerkin methods: An adapted biorthogonal wavelet basis
• Wavelet algorithms for numerical resolution of partial differential equations
• Polyharmonic cardinal splines: A minimization property
• OPERATOR-ADAPTED WAVELETS: CONNECTION WITH THE STRANG–FIX CONDITIONS
• Orthonormal bases of compactly supported wavelets
• Ten Lectures on Wavelets

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