The converse of Bohr's equivalence theorem with Fourier exponents linearly independent over the rational numbers
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http://hdl.handle.net/10045/122928
Títol: | The converse of Bohr's equivalence theorem with Fourier exponents linearly independent over the rational numbers |
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Autors: | Righetti, Mattia | Sepulcre, Juan Matias | Vidal, Tomás |
Grups d'investigació o GITE: | Curvas Alpha-Densas. Análisis y Geometría Local |
Centre, Departament o Servei: | Universidad de Alicante. Departamento de Matemáticas |
Paraules clau: | Bohr equivalence theorem | Dirichlet series | Converse theorem | Almost periodic functions |
Àrees de coneixement: | Análisis Matemático |
Data de publicació: | 9-d’abril-2022 |
Editor: | Elsevier |
Citació bibliogràfica: | Journal of Mathematical Analysis and Applications. 2022, 513(2): 126240. https://doi.org/10.1016/j.jmaa.2022.126240 |
Resum: | Given two arbitrary almost periodic functions with Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip V, where both functions assume the same set of values on every open vertical substrip included in V, is a necessary and sufficient condition for both functions to have the same region of almost periodicity and to be ⁎-equivalent or Bohr-equivalent. This result represents the converse of Bohr's equivalence theorem for this particular case. |
Patrocinadors: | The first author has been partially supported by a CRM-ISM postdoctoral fellowship and by a fellowship “Ing. Giorgio Schirillo” from INdAM. The second author's research has been partially supported by MICIU of Spain under project number PGC2018-097960-B-C22. |
URI: | http://hdl.handle.net/10045/122928 |
ISSN: | 0022-247X (Print) | 1096-0813 (Online) |
DOI: | 10.1016/j.jmaa.2022.126240 |
Idioma: | eng |
Tipus: | info:eu-repo/semantics/article |
Drets: | © 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Revisió científica: | si |
Versió de l'editor: | https://doi.org/10.1016/j.jmaa.2022.126240 |
Apareix a la col·lecció: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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