Completeness in \(L^1(\mathbb R)\) of discrete translates

DOI10.4171/RMI/447zbMath1104.42019arXivmath/0307323MaRDI QIDQ854543

Alexander Ulanovskii, Joaquim Bruna, Alexander Olevskiĭ

Publication date: 5 December 2006

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307323

zbMATH Keywords

generatoruniqueness setsBernstein classesBeurling-Malliavin density

Mathematics Subject Classification ID

Entire functions of one complex variable (general theory) (30D20) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Special classes of entire functions of one complex variable and growth estimates (30D15) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (11)

Completeness of discrete translates in the Hardy space 𝐻¹(ℝ) ⋮ On translates of the Poisson kernel and zeros of harmonic functions ⋮ Cyclicity of bicyclic operators ⋮ Schauder frames and completeness of translates in the Orlicz space ⋮ Unconditional Schauder frames of translates in \(L_p ( \mathbb{R}^d)\) ⋮ Reconstruction of Signals: Uniqueness and Stable Sampling ⋮ Beurling-Malliavin theory for Toeplitz kernels ⋮ Generating sets for Beurling algebras ⋮ Discrete translates in function spaces ⋮ Systems formed by translates of one element in $L_{p}(\mathbb R)$ ⋮ Poisson type generators for \(L^{1}(\mathbb R)\)

Cites Work

• Completeness of integer translates in function spaces on \(\mathbb{R}\)
• Density of Gabor frames
• Almost integer translates. Do nice generators exist?
• Completeness in L2(ℝ) of almost integer translates
• A sparse regular sequence of exponentials closed on large sets

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