Distributional Solutions of Nonhomogeneous Discrete and Continuous Refinement Equations

DOI10.1137/S0036141099350882zbMath0980.42035MaRDI QIDQ4509960

Zuowei Shen, Rong-Qing Jia, Qingtang Jiang

Publication date: 19 October 2000

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenesscompactly supported distributionsnonhomogeneous discrete and continuous refinement equations

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Integral transforms in distribution spaces (46F12) Numerical methods for wavelets (65T60) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (19)

Multi-window dilation-and-modulation frames on the half real line ⋮ Interpolatory quad/triangle subdivision schemes for surface design ⋮ Vector-stability of multiple vector refinable vectors ⋮ Multivariate nonhomogeneous refinement equations ⋮ Atomic functions: generalization to the multivariable case and promising applications ⋮ Probability distribution functions of the Grincevičjus series ⋮ The support of a refinable vector satisfying an inhomogeneous refinement equation ⋮ Approximation orders of shift-invariant subspaces of \(W_{2}^{s}(\mathbb R^d)\) ⋮ The spectral radius of matrix continuous refinement operators ⋮ Compactly supported distributional solutions of nonstationary nonhomogeneous refinement equations ⋮ Convergence of cascade algorithms in Sobolev spaces associated with multivariate refinement equations ⋮ Balanced multi-wavelets in $\mathbb R^s$ ⋮ Inhomogeneous refinement equations with random affine maps ⋮ Vector-Stability of Univariate Refinable Vectors ⋮ Multivariate refinement equations and convergence of cascade algorithms in \(L_p(0<p<1)\) spaces ⋮ Convergence rates of cascade algorithms associated with nonhomogeneous refinement equations ⋮ Vector-stability of refinable vectors ⋮ Regularity of anisotropic refinable functions ⋮ Convergence of cascade algorithms associated with nonhomogeneous refinement equations

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