Classical vs. non-Archimedean analysis: an approach via algebraic genericity

In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and ana...

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Detalhes bibliográficos
Autores: Fernández Sánchez, J., Maghsoudi, S., Rodríguez-Vidanes, D.L., Seoane Sepúlveda, Juan Benigno
Tipo de documento: artigo
Data de publicação:2022
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/71538
Acesso em linha:https://hdl.handle.net/20.500.14352/71538
Access Level:Acceso aberto
Palavra-chave:512.64
P-adic numbers
P-adic continuous function
P-adic differentiable function
P-adic sequences
Lineability
Algebrability
Spaceability
Cesàro summable
Non-absolutely convergent series
Liouville’s theorem
Lipschitz condition
Hahn–Banach theorem
Álgebra
Análisis funcional y teoría de operadores
Funciones (Matemáticas)
1201 Álgebra
1202 Análisis y Análisis Funcional
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oai_identifier_str oai:docta.ucm.es:20.500.14352/71538
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repository_id_str
spelling Classical vs. non-Archimedean analysis: an approach via algebraic genericityFernández Sánchez, J.Maghsoudi, S.Rodríguez-Vidanes, D.L.Seoane Sepúlveda, Juan Benigno512.64P-adic numbersP-adic continuous functionP-adic differentiable functionP-adic sequencesLineabilityAlgebrabilitySpaceabilityCesàro summableNon-absolutely convergent seriesLiouville’s theoremLipschitz conditionHahn–Banach theoremÁlgebraAnálisis funcional y teoría de operadoresFunciones (Matemáticas)1201 Álgebra1202 Análisis y Análisis FuncionalIn this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem.Springer NatureUniversidad Complutense de Madrid20222022-01-2920222022-01-29journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71538reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/715382026-06-02T12:44:21Z
dc.title.none.fl_str_mv Classical vs. non-Archimedean analysis: an approach via algebraic genericity
title Classical vs. non-Archimedean analysis: an approach via algebraic genericity
spellingShingle Classical vs. non-Archimedean analysis: an approach via algebraic genericity
Fernández Sánchez, J.
512.64
P-adic numbers
P-adic continuous function
P-adic differentiable function
P-adic sequences
Lineability
Algebrability
Spaceability
Cesàro summable
Non-absolutely convergent series
Liouville’s theorem
Lipschitz condition
Hahn–Banach theorem
Álgebra
Análisis funcional y teoría de operadores
Funciones (Matemáticas)
1201 Álgebra
1202 Análisis y Análisis Funcional
title_short Classical vs. non-Archimedean analysis: an approach via algebraic genericity
title_full Classical vs. non-Archimedean analysis: an approach via algebraic genericity
title_fullStr Classical vs. non-Archimedean analysis: an approach via algebraic genericity
title_full_unstemmed Classical vs. non-Archimedean analysis: an approach via algebraic genericity
title_sort Classical vs. non-Archimedean analysis: an approach via algebraic genericity
dc.creator.none.fl_str_mv Fernández Sánchez, J.
Maghsoudi, S.
Rodríguez-Vidanes, D.L.
Seoane Sepúlveda, Juan Benigno
author Fernández Sánchez, J.
author_facet Fernández Sánchez, J.
Maghsoudi, S.
Rodríguez-Vidanes, D.L.
Seoane Sepúlveda, Juan Benigno
author_role author
author2 Maghsoudi, S.
Rodríguez-Vidanes, D.L.
Seoane Sepúlveda, Juan Benigno
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.64
P-adic numbers
P-adic continuous function
P-adic differentiable function
P-adic sequences
Lineability
Algebrability
Spaceability
Cesàro summable
Non-absolutely convergent series
Liouville’s theorem
Lipschitz condition
Hahn–Banach theorem
Álgebra
Análisis funcional y teoría de operadores
Funciones (Matemáticas)
1201 Álgebra
1202 Análisis y Análisis Funcional
topic 512.64
P-adic numbers
P-adic continuous function
P-adic differentiable function
P-adic sequences
Lineability
Algebrability
Spaceability
Cesàro summable
Non-absolutely convergent series
Liouville’s theorem
Lipschitz condition
Hahn–Banach theorem
Álgebra
Análisis funcional y teoría de operadores
Funciones (Matemáticas)
1201 Álgebra
1202 Análisis y Análisis Funcional
description In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-29
2022
2022-01-29
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/71538
url https://hdl.handle.net/20.500.14352/71538
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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