Vector subdivision schemes and multiple wavelets

DOI10.1090/S0025-5718-98-00985-5zbMath0905.65139MaRDI QIDQ4210956

Ding-Xuan Zhou, Rong-Qing Jia, Sherman D. Riemenschneider

Publication date: 10 September 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

convergencetransition operatorsrefinement equationsrefinement maskjoint spectral radiimultiple refinable functionsvector subdivision schemesdouble waveletsmultiple wavelets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical methods for wavelets (65T60)

Related Items (48)

Riesz multiwavelet bases ⋮ Extension principles for dual multiwavelet frames of \(L_2(\mathbb R^s)\) constructed from multirefinable generators ⋮ Solutions of multiple vector refinement equations with infinite mask ⋮ Interpolatory rank-1 vector subdivision schemes ⋮ Convergence of multivariate non-stationary vector subdivision schemes ⋮ Vector subdivision schemes and their convergence for arbitrary matrix masks ⋮ Multivariate generalized Hermite subdivision schemes ⋮ Triangular \(\sqrt 3\)-subdivision schemes: The regular case ⋮ Correspondence between multiwavelet shrinkage and nonlinear diffusion ⋮ Convergence and error estimate of cascade algorithms with infinitely supported masks in \(L_p(\mathbb R^s)\) ⋮ Vector cascade algorithms with infinitely supported masks in weighted \(L_2\)-spaces ⋮ Vector cascade algorithms and refinable function vectors in Sobolev spaces ⋮ The limits of refinable functions ⋮ A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES ⋮ Multiple refinable Hermite interpolants ⋮ Convergence rate of vector subdivision scheme ⋮ Biorthogonal multiple wavelets generated by vector refinement equation ⋮ Vector refinement equations with infinitely supported masks ⋮ Subdivisions with infinitely supported mask ⋮ Subdivision schemes with polynomially decaying masks ⋮ Convergence of cascade algorithms in Sobolev spaces associated with multivariate refinement equations ⋮ \(L_p\) solutions of refinement equations ⋮ Convergence of subdivision schemes in \(L_p\) spaces ⋮ Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices ⋮ Regularity of multivariate vector subdivision schemes ⋮ On the joint spectral radius of matrices of order 2 with equal spectral radius ⋮ The independence of initial vectors in the subdivision schemes ⋮ Joint spectral radius and ternary Hermite subdivision ⋮ A generalization of the mean size formula of wavelet packets in \(L_p\) ⋮ Norms concerning subdivision sequences and their applications in wavelets ⋮ On stable refinable function vectors with arbitrary support ⋮ Interpolatory wavelets for manifold-valued data ⋮ Properties of locally linearly independent refinable function vectors ⋮ 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 ⋮ Inhomogeneous refinement equations ⋮ Convergence rates of cascade algorithms associated with nonhomogeneous refinement equations ⋮ Algebraic properties of subdivision operators with matrix mask and their applications ⋮ Riesz multiwavelet bases generated by vector refinement equation ⋮ Pointwise convergence of bounded cascade sequences ⋮ Convergence rates of vector cascade algorithms in \(L_p\) ⋮ Orthogonal multiwavelets of multiplicity four ⋮ Stability implies convergence of cascade algorithms in Sobolev space ⋮ Spectra of subdivision operators ⋮ Convergence of vector subdivision schemes in Sobolev spaces ⋮ Mean size of wavelet packets ⋮ Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks ⋮ Convergence of cascade algorithms associated with nonhomogeneous refinement equations

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