Completeness in L1(R) of discrete translates.

Bruna, Joaquim, Olevskii, Alexander, and Ulanovskii, Alexander. "Completeness in L1(R) of discrete translates.." Revista Matemática Iberoamericana 22.1 (2006): 1-16. <http://eudml.org/doc/41963>.

@article{Bruna2006,
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 ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.},
author = {Bruna, Joaquim, Olevskii, Alexander, Ulanovskii, Alexander},
journal = {Revista Matemática Iberoamericana},
keywords = {Análisis de Fourier; Espacios de Lebesgue; Completitud; Función entera; uniqueness sets; Bernstein classes; Beurling-Malliavin density; generator},
language = {eng},
number = {1},
pages = {1-16},
title = {Completeness in L1(R) of discrete translates.},
url = {http://eudml.org/doc/41963},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Bruna, Joaquim
AU - Olevskii, Alexander
AU - Ulanovskii, Alexander
TI - Completeness in L1(R) of discrete translates.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 1
SP - 1
EP - 16
AB - We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.
LA - eng
KW - Análisis de Fourier; Espacios de Lebesgue; Completitud; Función entera; uniqueness sets; Bernstein classes; Beurling-Malliavin density; generator
UR - http://eudml.org/doc/41963
ER -