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 |
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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. |
URI: | http://hdl.handle.net/10045/74790 |
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 |
Publisher version: | https://doi.org/10.1007/s11139-017-9950-1 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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2018_Sepulcre_Vidal_RamanujanJ_final.pdf | Versión final (acceso restringido) | 370,05 kB | Adobe PDF | Open Request a copy |
2018_Sepulcre_Vidal_RamanujanJ_revised.pdf | Versión revisada (acceso abierto) | 1,1 MB | Adobe PDF | Open Preview |
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