Completeness in $L^1(R)$ of discrete translates

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dc.creatorBruna, Joaquim
dc.creatorOlevskii, Alexander
dc.creatorUlanovskii, Alexander
dc.date2003-07-24
dc.date.accessioned2026-07-07T04:59:52Z
dc.date.available2026-07-07T04:59:52Z
dc.descriptionWe characterize, in terms of the Beurling-Malliavin density, the discrete spectra $Λ\subset\R$ for which a generator exists, that is a function $ϕ\in L^1(\R)$ such that its $Λ$-translates $ϕ(x-λ), λ\inΛ$, span $L^1(\R)$. It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra $Λ\subset\R$ which do not admit a single generator while they admit a pair of generators.
dc.description14 pages, submitted
dc.identifierhttps://arxiv.org/abs/math/0307323
dc.identifierhttp://arxiv.org/abs/math/0307323
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68163
dc.subjectClassical Analysis and ODEs
dc.subjectFunctional Analysis
dc.subject42A65;30D60
dc.titleCompleteness in $L^1(R)$ of discrete translates
dc.typetext

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