Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

Detalhes bibliográficos
Autor(a) principal: Castro, L. P.
Data de Publicação: 2016
Outros Autores: Saitoh, S., Yamada, A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/16216
Resumo: We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.
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spelling Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spacesReproducing kernelMoore-Penrose generalized inverseTikhonov regularizationHilbert-Schmidt operatorTensor product of Hilbert spacesGeneralized fractional functionBergman spaceSzegö spaceMultiplication operatorWe consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.Springer; Birkhäuser2018-07-20T14:00:56Z2016-12-01T00:00:00Z2016-122017-12-01T12:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16216eng1661-825410.1007/s11785-016-0545-4Castro, L. P.Saitoh, S.Yamada, A.info: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:RCAAP2024-02-22T11:30:07Zoai:ria.ua.pt:10773/16216Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:22.391147Repositório 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 Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
title Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
spellingShingle Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
Castro, L. P.
Reproducing kernel
Moore-Penrose generalized inverse
Tikhonov regularization
Hilbert-Schmidt operator
Tensor product of Hilbert spaces
Generalized fractional function
Bergman space
Szegö space
Multiplication operator
title_short Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
title_full Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
title_fullStr Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
title_full_unstemmed Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
title_sort Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces
author Castro, L. P.
author_facet Castro, L. P.
Saitoh, S.
Yamada, A.
author_role author
author2 Saitoh, S.
Yamada, A.
author2_role author
author
dc.contributor.author.fl_str_mv Castro, L. P.
Saitoh, S.
Yamada, A.
dc.subject.por.fl_str_mv Reproducing kernel
Moore-Penrose generalized inverse
Tikhonov regularization
Hilbert-Schmidt operator
Tensor product of Hilbert spaces
Generalized fractional function
Bergman space
Szegö space
Multiplication operator
topic Reproducing kernel
Moore-Penrose generalized inverse
Tikhonov regularization
Hilbert-Schmidt operator
Tensor product of Hilbert spaces
Generalized fractional function
Bergman space
Szegö space
Multiplication operator
description We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.
publishDate 2016
dc.date.none.fl_str_mv 2016-12-01T00:00:00Z
2016-12
2017-12-01T12:00:00Z
2018-07-20T14:00:56Z
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/10773/16216
url http://hdl.handle.net/10773/16216
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1661-8254
10.1007/s11785-016-0545-4
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; Birkhäuser
publisher.none.fl_str_mv Springer; Birkhäuser
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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