- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:44
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
22
2006
1
Completeness in $L^1 (\mathbb R)$ of discrete translates
Joaquim
Bruna
Universitat Autonoma de Barcelona, BELLATERRA, SPAIN
Alexander
Olevskii
Tel Aviv University, RAMAT AVIV, TEL AVIV, ISRAEL
Alexander
Ulanovskii
Stavanger University College, STAVANGER, NORWAY
Discrete translates, generator, Beurling-Malliavin density, uniqueness sets, Bernstein classes
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.
Fourier analysis
Functions of a complex variable
General
1
16
10.4171/RMI/447
http://www.ems-ph.org/doi/10.4171/RMI/447