Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

DOI10.1006/jath.2002.3682zbMath1017.42029OpenAlexW2138444111MaRDI QIDQ1867517

Di-Rong Chen, Gerlind Plonka-Hoch

Publication date: 2 April 2003

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

Full work available at URL: https://doi.org/10.1006/jath.2002.3682

zbMATH Keywords

Sobolev spacerefinable functionjoint spectral radiuscascade algorithmtensor product \(B\)-spline function

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) Spline approximation (41A15)

Related Items (7)

Convergent bivariate subdivision scheme with nonnegative mask whose support is non-convex ⋮ Convergence and error estimate of cascade algorithms with infinitely supported masks in \(L_p(\mathbb R^s)\) ⋮ Convergence of irregular Hermite subdivision schemes ⋮ Vector cascade algorithms and refinable function vectors in Sobolev spaces ⋮ A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES ⋮ Characterization of Riesz bases of wavelets generated from multiresolution analysis ⋮ Pointwise convergence of bounded cascade sequences

Cites Work

• Shift-invariant spaces and linear operator equations
• Algebraic properties of subdivision operators with matrix mask and their applications
• On vector subdivision
• Regularity of multiwavelets
• Convergence of multidimensional cascade algorithm
• Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets
• Convergence of vector subdivision schemes in Sobolev spaces
• Subdivision schemes in \(L_ p\) spaces
• How does truncation of the mask affect a refinable function?
• Stationary subdivision
• Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
• Multivariate Refinement Equations and Convergence of Subdivision Schemes
• Vector subdivision schemes and multiple wavelets
• Multivariate matrix refinable functions with arbitrary matrix dilation
• Characterizations of Scaling Functions: Continuous Solutions
• Wavelet Analysis of Refinement Equations
• Approximation properties of multivariate wavelets
• Refinable Function Vectors
• Norms concerning subdivision sequences and their applications in wavelets
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