Stability of the shifts of a finite number of functions

DOI10.1006/jath.1998.3215zbMath0957.42019OpenAlexW1973578161MaRDI QIDQ1273407

Rong-Qing Jia

Publication date: 25 March 2001

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

Full work available at URL: https://semanticscholar.org/paper/bba5d8c30db2f33d7c259b55c0b22b9b5d11949e

zbMATH Keywords

stabilityRiesz basisHardy spacesshift-invariant spacesdiscrete convolution

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) (H^p)-spaces (42B30) Hyperfunctions, analytic functionals (46F15) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (18)

The closedness of shift invariant subspaces in \(L^{p,q}(\mathbb{R}^{d+1})\) ⋮ The \(L^{p,q}\)-stability of the shifts of finitely many functions in mixed Lebesgue spaces \(L^{p,q}(\mathbb R^{d+1})\) ⋮ Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data ⋮ Locally finite dimensional shift-invariant spaces in $\mathbf {R}^d$ ⋮ \(L_p\)-solutions of vector refinement equations with general dilation matrix ⋮ Convolution random sampling in multiply generated shift-invariant spaces of \(L^p(\mathbb{R}^d)\) ⋮ The Structure of Finitely Generated Shift-Invariant Subspaces in Super Hilbert Spaces ⋮ Affine synthesis onto \(L^p\) when \(0< p \leq 1\) ⋮ Frames for weighted shift-invariant spaces ⋮ A generalization of the mean size formula of wavelet packets in \(L_p\) ⋮ 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 ⋮ Compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces ⋮ Riesz multiwavelet bases generated by vector refinement equation ⋮ Convergence rates of vector cascade algorithms in \(L_p\) ⋮ Minimal generator sets for finitely generated shift-invariant subspaces of \(L^{2}(\mathbb R^{n})\) ⋮ Stability implies convergence of cascade algorithms in Sobolev space ⋮ Convergence of vector subdivision schemes in Sobolev spaces

Cites Work

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• Local linear independence of the translates of a box spline
• Shift-invariant spaces and linear operator equations
• A Bernstein-type inequality associated with wavelet decomposition
• On the local linear independence of translates of a box spline
• Compression of Wavelet Decompositions
• On linear independence for integer translates of a finite number of functions

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