The Toeplitz Theorem and its Applications to Approximation Theory and Linear PDE's

DOI10.2307/2154840zbMath0823.41009OpenAlexW4230797325MaRDI QIDQ4846045

Rong-Qing Jia

Publication date: 23 October 1995

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/3c71ae9ecf0fb83aa55cd164841a2e0dd47825ca

zbMATH Keywords

partial differential equationsapproximation orderpartial difference equationsinfinite systems of linear equationsshift- invariant spaces

Mathematics Subject Classification ID

Additive difference equations (39A10) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Linear equations (linear algebraic aspects) (15A06) General topics in partial differential equations (35A99)

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Shift-invariant spaces of tempered distributions and \(L_{p}\)-functions ⋮ Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces ⋮ Partition of unity and density: A counterexample ⋮ Sparse approximate solution of fitting surface to scattered points by MLASSO model ⋮ Study on the generator \(f\) of the operators \(I_n\) and \(I_t\) ⋮ Approximation properties of wavelets on p-adic fields ⋮ Average sampling in shift invariant subspaces with symmetric averaging functions ⋮ The aliasing error in recovery of nonbandlimited signals by prefiltering and sampling ⋮ Approximation properties of multivariate wavelets ⋮ Scattered date interpolation from principal shift-invariant spaces ⋮ The structure of finitely generated shift-invariant spaces in mixed Lebesgue spaces \(L^{p,q}\left( {\mathbb{R}}^{d+1}\right)\) ⋮ Shift-invariant spaces and linear operator equations ⋮ Scattered data reconstruction by regularization in B-spline and associated wavelet spaces ⋮ Characterizations of principal shift-invariant spaces.

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