Completeness of integer translates in function spaces on \(\mathbb{R}\)

DOI10.1006/jath.1996.0106zbMath0872.46021OpenAlexW2065065158MaRDI QIDQ1352901

Aharon Atzmon, Alexander Olevskiĭ

Publication date: 12 October 1997

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

Full work available at URL: https://doi.org/10.1006/jath.1996.0106

zbMATH Keywords

generatorsweighted function spacesrearrangement invariant spacescomposition operatorinteger translatesuniqueness setsMarcinkiewiczWiener Tauberian theoremLorentz\(\mathbb{Z}\)-cyclic elementsOrliczproblem of completeness

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (19)

The geometry of sets of parameters of wave packet frames ⋮ Completeness of discrete translates in the Hardy space 𝐻¹(ℝ) ⋮ Completeness in \(L^1(\mathbb R)\) of discrete translates ⋮ Schauder frames and completeness of translates in the Orlicz space ⋮ Unconditional Schauder frames of translates in \(L_p ( \mathbb{R}^d)\) ⋮ Reconstruction of Signals: Uniqueness and Stable Sampling ⋮ Upper Beurling density of systems formed by translates of finite sets of elements in \(L^p(\mathbb{R}^d)\) ⋮ Unconditional structures of translates for \(L_p(\mathbb R^d)\) ⋮ Cyclic composition operators on separable locally compact metric spaces ⋮ A Schauder basis for \(L_2\) consisting of non-negative functions ⋮ On the structure and interpolation properties of quasi shift-invariant spaces ⋮ Perturbations in Müntz's theorem ⋮ Generating sets for Beurling algebras ⋮ Spectral subspaces of $L^p$ for $p<1$ ⋮ Discrete translates in function spaces ⋮ On the completeness and other properties of some function systems in \(L_p\), \(0<p<\infty\) ⋮ Haar approximation from within for \(L^p(\mathbb{R}^d)\), \(0<p<1\) ⋮ Systems formed by translates of one element in $L_{p}(\mathbb R)$ ⋮ Remarks concerning completeness of translates in function spaces

This page was built for publication: Completeness of integer translates in function spaces on \(\mathbb{R}\)