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

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dc.contributor.authorFernández Sánchez, J.
dc.contributor.authorMaghsoudi, S.
dc.contributor.authorRodríguez-Vidanes, D.L.
dc.contributor.authorSeoane Sepúlveda, Juan Benigno
dc.date.accessioned2023-06-22T10:44:02Z
dc.date.available2023-06-22T10:44:02Z
dc.date.issued2022-01-29
dc.descriptionCRUE-CSIC (Acuerdos Transformativos 2022)
dc.description.abstractIn 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipIran National Science Foundation (INSF)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/72536
dc.identifier.doi10.1007/s13398-022-01209-5
dc.identifier.issn1578-7303
dc.identifier.officialurlhttps://doi.org/10.1007/s13398-022-01209-5
dc.identifier.urihttps://hdl.handle.net/20.500.14352/71538
dc.issue.number2
dc.journal.titleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
dc.language.isoeng
dc.publisherSpringer Nature
dc.relation.projectIDPGC2018-097286-B-I00; PRE2019-089135
dc.relation.projectID99019850
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu512.64
dc.subject.keywordP-adic numbers
dc.subject.keywordP-adic continuous function
dc.subject.keywordP-adic differentiable function
dc.subject.keywordP-adic sequences
dc.subject.keywordLineability
dc.subject.keywordAlgebrability
dc.subject.keywordSpaceability
dc.subject.keywordCesàro summable
dc.subject.keywordNon-absolutely convergent series
dc.subject.keywordLiouville’s theorem
dc.subject.keywordLipschitz condition
dc.subject.keywordHahn–Banach theorem
dc.subject.ucmÁlgebra
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.subject.ucmFunciones (Matemáticas)
dc.subject.unesco1201 Álgebra
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleClassical vs. non-Archimedean analysis: an approach via algebraic genericity
dc.typejournal article
dc.volume.number116
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