Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets

DOI10.1007/s002110100265zbMath1019.65108OpenAlexW2025017973MaRDI QIDQ1601751

R. Smith

Publication date: 27 June 2002

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002110100265

zbMATH Keywords

waveletsconvergencestrong convergenceSobolev spacestransition operatorrefinement equationrefinable functionscascade algorithmsubdivision operatorcomputation of integralsisotropic dilation

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) Numerical methods for wavelets (65T60) Numerical quadrature and cubature formulas (65D32)

Related Items

Vector cascade algorithms and refinable function vectors in Sobolev spaces ⋮ Vector multivariate subdivision schemes: comparison of spectral methods for their regularity analysis ⋮ A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES ⋮ Convergence rate of vector subdivision scheme ⋮ Characterization of Riesz bases of wavelets generated from multiresolution analysis ⋮ Convergence of cascade algorithms in Sobolev spaces associated with multivariate refinement equations ⋮ Concerning order of convergence for subdivision ⋮ Scalar multivariate subdivision schemes and box splines ⋮ Norms concerning subdivision sequences and their applications in wavelets ⋮ Pseudo box splines ⋮ Stability implies convergence of cascade algorithms in Sobolev space ⋮ Convergence of vector subdivision schemes in Sobolev spaces ⋮ Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks