Riemann–Hilbert problems, Toeplitz operators and Q-classes

Detalhes bibliográficos
Autor(a) principal: Câmara, M. C.
Data de Publicação: 2014
Outros Autores: Malheiro, Teresa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/32347
Resumo: We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.
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spelling Riemann–Hilbert problems, Toeplitz operators and Q-classesRiemann–Hilbert problemsToeplitz operatorsFactorizationmatrix equationsCiências Naturais::MatemáticasScience & TechnologyWe generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.Fundação para a Ciência e a Tecnologia (FCT/Portugal), through Project PTDC/MAT/121837/2010 and Project Est- C/MAT/UI0013/2011. The first author was also supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems and the second author was also supported by the Centre of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPETESpringerUniversidade do MinhoCâmara, M. C.Malheiro, Teresa2014-10-012014-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/32347eng1420-898910.1007/s00020-014-2140-2http://link.springer.com/article/10.1007%2Fs00020-014-2140-2info: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:RCAAP2023-07-21T12:43:33Zoai:repositorium.sdum.uminho.pt:1822/32347Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:41:03.462866Repositório 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 Riemann–Hilbert problems, Toeplitz operators and Q-classes
title Riemann–Hilbert problems, Toeplitz operators and Q-classes
spellingShingle Riemann–Hilbert problems, Toeplitz operators and Q-classes
Câmara, M. C.
Riemann–Hilbert problems
Toeplitz operators
Factorization
matrix equations
Ciências Naturais::Matemáticas
Science & Technology
title_short Riemann–Hilbert problems, Toeplitz operators and Q-classes
title_full Riemann–Hilbert problems, Toeplitz operators and Q-classes
title_fullStr Riemann–Hilbert problems, Toeplitz operators and Q-classes
title_full_unstemmed Riemann–Hilbert problems, Toeplitz operators and Q-classes
title_sort Riemann–Hilbert problems, Toeplitz operators and Q-classes
author Câmara, M. C.
author_facet Câmara, M. C.
Malheiro, Teresa
author_role author
author2 Malheiro, Teresa
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Câmara, M. C.
Malheiro, Teresa
dc.subject.por.fl_str_mv Riemann–Hilbert problems
Toeplitz operators
Factorization
matrix equations
Ciências Naturais::Matemáticas
Science & Technology
topic Riemann–Hilbert problems
Toeplitz operators
Factorization
matrix equations
Ciências Naturais::Matemáticas
Science & Technology
description We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.
publishDate 2014
dc.date.none.fl_str_mv 2014-10-01
2014-10-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/32347
url http://hdl.handle.net/1822/32347
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1420-8989
10.1007/s00020-014-2140-2
http://link.springer.com/article/10.1007%2Fs00020-014-2140-2
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
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