Completeness in L^1(R) of discrete translates

• Autores: Joaquim Bruna i Floris , Alexander Olevskii, Alexander Ulanovskii
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 1, 2006, págs. 1-16
• Idioma: inglés
• DOI: 10.4171/rmi/447
• Títulos paralelos:
  • Completitud en L1(R) de trasladados discretos
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• Resumen

  • We characterize, in terms of the Beurling-Malliavin density, the discrete spectra ? Ì R for which a generator exists, that is a function f Î L1(R) such that its ? translates f(x - ?), ? Î ?, 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 ? Î R which do not admit a single generator while they admit a pair of generators.