Bohr’s equivalence relation in the space of Besicovitch almost periodic functions

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Title: Bohr’s equivalence relation in the space of Besicovitch almost periodic functions
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 | Besicovitch almost periodic functions | Bochner’s theorem | Exponential sums | Fourier series
Knowledge Area: Análisis Matemático
Issue Date: Aug-2019
Publisher: Springer US
Citation: The Ramanujan Journal. 2019, 49(3): 625-639. doi:10.1007/s11139-018-0022-y
Abstract: Based on Bohr’s equivalence relation which was established for general Dirichlet series, in this paper we introduce a new equivalence relation on the space of almost periodic functions in the sense of Besicovitch, B(R,C), defined in terms of polynomial approximations. From this, we show that in an important subspace B2(R,C)⊂B(R,C), where Parseval’s equality and the Riesz–Fischer theorem hold, its equivalence classes are sequentially compact and the family of translates of a function belonging to this subspace is dense in its own class.
ISSN: 1382-4090 (Print) | 1572-9303 (Online)
DOI: 10.1007/s11139-018-0022-y
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Science+Business Media, LLC, part of Springer Nature 2018
Peer Review: si
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Appears in Collections:INV - CADAGL - Artículos de Revistas

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