# Completeness in L1(R) of discrete translates.

Joaquim Bruna; Alexander Olevskii; Alexander Ulanovskii

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 1, page 1-16
- ISSN: 0213-2230

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topBruna, 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 -

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