ar X iv : m at h / 03 07 32 3 v 1 [ m at h . C A ] 2 4 Ju l 2 00 3 COMPLETENESS IN L 1 ( R ) OF DISCRETE TRANSLATES

Abstract

We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L(R) such that its Λ-translates φ(x − λ), λ ∈ Λ, span L(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra Λ ⊂ R which do not admit a single generator while they admit a pair of generators.

Cite this paper

@inproceedings{Ulanovskii2003arXI, title={ar X iv : m at h / 03 07 32 3 v 1 [ m at h . C A ] 2 4 Ju l 2 00 3 COMPLETENESS IN L 1 ( R ) OF DISCRETE TRANSLATES}, author={Alexander Ulanovskii}, year={2003} }