Tópicos de análise funcional (vias clássica e não-standard)
Autor(a) principal: | |
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Data de Publicação: | 2002 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/15063 |
Resumo: | This thesis concerns aspects of the functional analysis from both the classical and the nonstandard viewpoints. Nowadays functional analysis plays an increasing role in the applied sciences as well as in mathematics itself. Besides deepening the study of the subject itself, from a classical point of view, we took the opportunity to analyse some questions and try to make some proofs by the methods of nonstandard analysis, by applying some notions and techniques learned in the Master of Science in Applied Mathematics course on Nonstandard Analysis. We begin by presenting the Nonstandard Analysis axiomatic foundations (Nelson’s axiomatics), make some immediate applications to the real line and give nonstandard (or external) characterizations of several notions, namely the shadow of a real number and the limit of a sequence of real numbers. In order to study the spectral theory we also present some topological notions needed in a nonstandard framework. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Tópicos de análise funcional (vias clássica e não-standard)Matemática aplicadaAnálise funcionalThis thesis concerns aspects of the functional analysis from both the classical and the nonstandard viewpoints. Nowadays functional analysis plays an increasing role in the applied sciences as well as in mathematics itself. Besides deepening the study of the subject itself, from a classical point of view, we took the opportunity to analyse some questions and try to make some proofs by the methods of nonstandard analysis, by applying some notions and techniques learned in the Master of Science in Applied Mathematics course on Nonstandard Analysis. We begin by presenting the Nonstandard Analysis axiomatic foundations (Nelson’s axiomatics), make some immediate applications to the real line and give nonstandard (or external) characterizations of several notions, namely the shadow of a real number and the limit of a sequence of real numbers. In order to study the spectral theory we also present some topological notions needed in a nonstandard framework.Universidade de Évora2015-08-31T16:51:53Z2015-08-312002-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10174/15063http://hdl.handle.net/10174/15063pordep C.T.rsilva@eseb.ipbeja.pt333Silva, Romeu Vieira dainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:00:15Zoai:dspace.uevora.pt:10174/15063Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:07:28.818865Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Tópicos de análise funcional (vias clássica e não-standard) |
title |
Tópicos de análise funcional (vias clássica e não-standard) |
spellingShingle |
Tópicos de análise funcional (vias clássica e não-standard) Silva, Romeu Vieira da Matemática aplicada Análise funcional |
title_short |
Tópicos de análise funcional (vias clássica e não-standard) |
title_full |
Tópicos de análise funcional (vias clássica e não-standard) |
title_fullStr |
Tópicos de análise funcional (vias clássica e não-standard) |
title_full_unstemmed |
Tópicos de análise funcional (vias clássica e não-standard) |
title_sort |
Tópicos de análise funcional (vias clássica e não-standard) |
author |
Silva, Romeu Vieira da |
author_facet |
Silva, Romeu Vieira da |
author_role |
author |
dc.contributor.author.fl_str_mv |
Silva, Romeu Vieira da |
dc.subject.por.fl_str_mv |
Matemática aplicada Análise funcional |
topic |
Matemática aplicada Análise funcional |
description |
This thesis concerns aspects of the functional analysis from both the classical and the nonstandard viewpoints. Nowadays functional analysis plays an increasing role in the applied sciences as well as in mathematics itself. Besides deepening the study of the subject itself, from a classical point of view, we took the opportunity to analyse some questions and try to make some proofs by the methods of nonstandard analysis, by applying some notions and techniques learned in the Master of Science in Applied Mathematics course on Nonstandard Analysis. We begin by presenting the Nonstandard Analysis axiomatic foundations (Nelson’s axiomatics), make some immediate applications to the real line and give nonstandard (or external) characterizations of several notions, namely the shadow of a real number and the limit of a sequence of real numbers. In order to study the spectral theory we also present some topological notions needed in a nonstandard framework. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-01-01T00:00:00Z 2015-08-31T16:51:53Z 2015-08-31 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/15063 http://hdl.handle.net/10174/15063 |
url |
http://hdl.handle.net/10174/15063 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
dep C.T. rsilva@eseb.ipbeja.pt 333 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de Évora |
publisher.none.fl_str_mv |
Universidade de Évora |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799136559539159040 |