Open Access
May, 2006 Completeness in $L^1 (\mathbb R)$ of discrete translates
Joaquim Bruna , Alexander Olevskii , Alexander Ulanovskii
Rev. Mat. Iberoamericana 22(1): 1-16 (May, 2006).


We characterize, in terms of the Beurling-Malliavin density, the discrete spectra $\Lambda\subset\mathbb R$ for which a generator exists, that is a function $\varphi\in L^1(\mathbb R)$ such that its $\Lambda$-translates $\varphi(x-\lambda), \lambda\in\Lambda$, span $L^1(\mathbb R)$. It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra $\Lambda\subset\mathbb R$ which do not admit a single generator while they admit a pair of generators.


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Joaquim Bruna . Alexander Olevskii . Alexander Ulanovskii . "Completeness in $L^1 (\mathbb R)$ of discrete translates." Rev. Mat. Iberoamericana 22 (1) 1 - 16, May, 2006.


Published: May, 2006
First available in Project Euclid: 24 May 2006

zbMATH: 1104.42019
MathSciNet: MR2267311

Primary: 30D15 , 30D20 , 42A65 , 42C30

Keywords: Bernstein classes , Beurling-Malliavin density , discrete translates , generator , uniqueness sets

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.22 • No. 1 • May, 2006
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