A lot of “counterexamples” to Liouville's theorem
We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, it is sh...
| Autor: | |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 1996 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87504 |
| Acceso en línea: | https://hdl.handle.net/11441/87504 https://doi.org/10.1006/jmaa.1996.0298 |
| Access Level: | acceso abierto |
| Palabra clave: | Liouville’s theorem Entire functions Dense linear manifold Radon transform Arakelian set Strips and sectors Growth index |
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A lot of “counterexamples” to Liouville's theoremBernal González, LuisLiouville’s theoremEntire functionsDense linear manifoldRadon transformArakelian setStrips and sectorsGrowth indexWe prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, it is shown the existence of an entire function with infinite growth index satisfying the latter property.Dirección General de Investigación Científica y Técnica (DGICYT). EspañaElsevierAnálisis MatemáticoFQM127: Análisis Funcional no Lineal1996info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87504https://doi.org/10.1006/jmaa.1996.0298reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Analysis and Applications, 201 (3), 1002-1009.PB93-0926https://reader.elsevier.com/reader/sd/pii/S0022247X9690298X?token=56B319762D841EA68B663502C246A6E4E4B7B47CC0CA10AA7485A719E746640B8A365325E76230250B5BC8C8EE576445info:eu-repo/semantics/openAccessoai:idus.us.es:11441/875042026-06-17T12:51:07Z |
| dc.title.none.fl_str_mv |
A lot of “counterexamples” to Liouville's theorem |
| title |
A lot of “counterexamples” to Liouville's theorem |
| spellingShingle |
A lot of “counterexamples” to Liouville's theorem Bernal González, Luis Liouville’s theorem Entire functions Dense linear manifold Radon transform Arakelian set Strips and sectors Growth index |
| title_short |
A lot of “counterexamples” to Liouville's theorem |
| title_full |
A lot of “counterexamples” to Liouville's theorem |
| title_fullStr |
A lot of “counterexamples” to Liouville's theorem |
| title_full_unstemmed |
A lot of “counterexamples” to Liouville's theorem |
| title_sort |
A lot of “counterexamples” to Liouville's theorem |
| dc.creator.none.fl_str_mv |
Bernal González, Luis |
| author |
Bernal González, Luis |
| author_facet |
Bernal González, Luis |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Análisis Matemático FQM127: Análisis Funcional no Lineal |
| dc.subject.none.fl_str_mv |
Liouville’s theorem Entire functions Dense linear manifold Radon transform Arakelian set Strips and sectors Growth index |
| topic |
Liouville’s theorem Entire functions Dense linear manifold Radon transform Arakelian set Strips and sectors Growth index |
| description |
We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, it is shown the existence of an entire function with infinite growth index satisfying the latter property. |
| publishDate |
1996 |
| dc.date.none.fl_str_mv |
1996 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion |
| format |
article |
| status_str |
submittedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/11441/87504 https://doi.org/10.1006/jmaa.1996.0298 |
| url |
https://hdl.handle.net/11441/87504 https://doi.org/10.1006/jmaa.1996.0298 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Journal of Mathematical Analysis and Applications, 201 (3), 1002-1009. PB93-0926 https://reader.elsevier.com/reader/sd/pii/S0022247X9690298X?token=56B319762D841EA68B663502C246A6E4E4B7B47CC0CA10AA7485A719E746640B8A365325E76230250B5BC8C8EE576445 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier |
| publisher.none.fl_str_mv |
Elsevier |
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reponame:idUS. Depósito de Investigación de la Universidad de Sevilla instname:Universidad de Sevilla (US) |
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Universidad de Sevilla (US) |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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1869410530691645440 |
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15,300724 |