Inhomogeneous refinement equations

DOI10.1007/BF02479677zbMath0932.42026OpenAlexW2014776486MaRDI QIDQ1282027

Gilbert Strang, Ding-Xuan Zhou

Publication date: 28 March 1999

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59592

zbMATH Keywords

waveletsjoint spectral radiusinhomogeneous refinement equationcascade algorithmmaskmultiple refinable functions

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Rate of convergence, degree of approximation (41A25)

Related Items (20)

Multi-window dilation-and-modulation frames on the half real line ⋮ Inhomogeneous poly-scale refinement type equations and Markov operators with perturbations ⋮ Interpolatory quad/triangle subdivision schemes for surface design ⋮ The limits of refinable functions ⋮ Multiple refinable Hermite interpolants ⋮ Multivariate nonhomogeneous refinement equations ⋮ Probability distribution functions of the Grincevičjus series ⋮ The support of a refinable vector satisfying an inhomogeneous refinement equation ⋮ Compactly supported distributional solutions of nonstationary nonhomogeneous refinement equations ⋮ Convergence of cascade algorithms in Sobolev spaces associated with multivariate refinement equations ⋮ Computational approach to solvability of refinement equations ⋮ Norms concerning subdivision sequences and their applications in wavelets ⋮ Biorthogonal interpolatory multiscaling functions and corresponding multiwavelets ⋮ Inhomogeneous refinement equations with random affine maps ⋮ Multivariate refinement equations and convergence of cascade algorithms in \(L_p(0<p<1)\) spaces ⋮ Convergence of cascade algorithms in Sobolev spaces associated with inhomogeneous refinement equations ⋮ Convergence rates of cascade algorithms associated with nonhomogeneous refinement equations ⋮ Regularity of anisotropic refinable functions ⋮ Spectra of subdivision operators ⋮ Mean size of wavelet packets

Cites Work

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• Fractal functions and wavelet expansions based on several scaling functions
• Existence of multiple refinable distributions
• Subdivision schemes in \(L_ p\) spaces
• Approximation by translates of refinable functions
• Multivariate nonhomogeneous refinement equations
• Compactly supported solutions of functional-differential equations and their applications
• Ten Lectures on Wavelets
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• Vector subdivision schemes and multiple wavelets
• Shift-invariant spaces on the real line
• Approximation by Multiple Refinable Functions
• Characterization of $L^p $-Solutions for the Two-Scale Dilation Equations

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