Almost periodic functions in terms of Bohr’s equivalence relation

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Title: Almost periodic functions in terms of Bohr’s equivalence relation
Authors: Sepulcre, Juan Matias | Vidal, Tomás
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Almost periodic functions | Exponential sums | Riemann zeta function | Bochner’s theorem | Fourier series | Dirichlet series
Knowledge Area: Análisis Matemático
Issue Date: May-2018
Publisher: Springer Science+Business Media, LLC
Citation: The Ramanujan Journal. 2018, 46(1): 245-267. doi:10.1007/s11139-017-9950-1
Abstract: In this paper we introduce an equivalence relation on the classes of almost periodic functions of a real or complex variable which is used to refine Bochner’s result that characterizes these spaces of functions. In fact, with respect to the topology of uniform convergence, we prove that the limit points of the family of translates of an almost periodic function are precisely the functions which are equivalent to it, which leads us to a characterization of almost periodicity. In particular we show that any exponential sum which is equivalent to the Riemann zeta function, ζ(s), can be uniformly approximated in {s = σ +i t : σ > 1} by certain vertical translates of ζ(s).
Sponsor: The first author’s research was partially supported by Generalitat Valenciana under Project GV/2015/035.
ISSN: 1382-4090 (Print) | 1572-9303 (Online)
DOI: 10.1007/s11139-017-9950-1
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Science+Business Media, LLC 2017
Peer Review: si
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Appears in Collections:INV - CADAGL - Artículos de Revistas

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