The class of c-almost periodic functions defined on vertical strips in the complex plane
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Título: | The class of c-almost periodic functions defined on vertical strips in the complex plane |
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Autor/es: | Ounis, Hadjer | Sepulcre, Juan Matias |
Grupo/s de investigación o GITE: | Curvas Alpha-Densas. Análisis y Geometría Local |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Almost periodic functions | c-almost periodic functions | Almost anti-periodic functions | Functions of a complex variable |
Área/s de conocimiento: | Análisis Matemático |
Fecha de publicación: | 16-jun-2022 |
Editor: | Springer Nature |
Cita bibliográfica: | Revista Matemática Complutense. 2023, 36: 707-724. https://doi.org/10.1007/s13163-022-00433-2 |
Resumen: | In this paper, we develop the notion of c-almost periodicity for functions defined on vertical strips in the complex plane. As a generalization of Bohr’s concept of almost periodicity, we study the main properties of this class of functions which was recently introduced for the case of one real variable. In fact, we extend some important results of this theory which were already demonstrated for some particular cases. In particular, given a non-null complex number c, we prove that the family of vertical translates of a prefixed c-almost periodic function defined in a vertical strip U is relatively compact on any vertical substrip of U, which leads to proving that every c-almost periodic function is also almost periodic and, in fact, cm-almost periodic for each integer number m. |
Patrocinador/es: | Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first author was supported by 076 Bis/PG/Espagne/2020-2021 (Ministère de l’Enseignement Supérieur et de la Recherche Scientifique). The second and corresponding author was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE). |
URI: | http://hdl.handle.net/10045/124323 |
ISSN: | 1139-1138 (Print) | 1988-2807 (Online) |
DOI: | 10.1007/s13163-022-00433-2 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1007/s13163-022-00433-2 |
Aparece en las colecciones: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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