Bochner-Type Property on Spaces of Generalized Almost Periodic Functions
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http://hdl.handle.net/10045/109984
Title: | Bochner-Type Property on Spaces of Generalized Almost Periodic Functions |
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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 | Besicovitch almost periodic functions | Stepanov almost periodic functions | Weyl almost periodic functions | Bochner’s theorem | Approximation by trigonometric polynomials | Exponential sums | Fourier series | Bohr’s equivalence relation |
Knowledge Area: | Análisis Matemático |
Issue Date: | 27-Oct-2020 |
Publisher: | Springer Nature |
Citation: | Mediterranean Journal of Mathematics. 2020, 17:193. https://doi.org/10.1007/s00009-020-01628-x |
Abstract: | Our paper is focused on spaces of generalized almost periodic functions which, as in classical Fourier analysis, are associated with a Fourier series with real frequencies. In fact, based on a pertinent equivalence relation defined on the spaces of almost periodic functions in Bohr, Stepanov, Weyl and Besicovitch’s sense, we refine the Bochner-type property by showing that the condition of almost periodicity of a function in any of these generalized spaces can be interpreted in the way that, with respect to the topology of each space, the closure of its set of translates coincides with its corresponding equivalence class. |
Sponsor: | The first author’s research was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE). |
URI: | http://hdl.handle.net/10045/109984 |
ISSN: | 1660-5446 (Print) | 1660-5454 (Online) |
DOI: | 10.1007/s00009-020-01628-x |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer Nature Switzerland AG 2020 |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s00009-020-01628-x |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
Files in This Item:
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Sepulcre_Vidal_2020_MediterrJMath_final.pdf | Versión final (acceso restringido) | 424,75 kB | Adobe PDF | Open Request a copy |
Sepulcre_Vidal_2020_MediterrJMath_preprint.pdf | Preprint (acceso abierto) | 291,9 kB | Adobe PDF | Open Preview |
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