Orthogonally additive holomorphic functions of bounded type over C(K)

Autores
Carando, Daniel Germán; Lassalle, Silvia Beatriz; Zalduendo, Ignacio Martin
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form f(x)=∫Kh(x)dμ for some μ and holomorphic h : C (K) → L1(μ) of bounded type.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lassalle, Silvia Beatriz. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Materia
HOLOMORPHIC FUNCTIONS OVER C(K)
INTEGRAL REPRESENTATION
ORTHOGONALLY ADDITIVE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98725
Acceder
id CONICETDig_0d2d8880d31620c5f9e16ebc985ec3f8
oai_identifier_str oai:ri.conicet.gov.ar:11336/98725
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Orthogonally additive holomorphic functions of bounded type over C(K)Carando, Daniel GermánLassalle, Silvia BeatrizZalduendo, Ignacio MartinHOLOMORPHIC FUNCTIONS OVER C(K)INTEGRAL REPRESENTATIONORTHOGONALLY ADDITIVEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form f(x)=∫Kh(x)dμ for some μ and holomorphic h : C (K) → L1(μ) of bounded type.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaCambridge University Press2010-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98725Carando, Daniel Germán; Lassalle, Silvia Beatriz; Zalduendo, Ignacio Martin; Orthogonally additive holomorphic functions of bounded type over C(K); Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 53; 3; 10-2010; 609-6180013-0915CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/orthogonally-additive-holomorphic-functions-of-bounded-type-over-ck/B9719DF1CC1E0AB4274182C32428050Dinfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0013091509000248info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:02:07Zoai:ri.conicet.gov.ar:11336/98725instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:02:07.677CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Orthogonally additive holomorphic functions of bounded type over C(K)
title Orthogonally additive holomorphic functions of bounded type over C(K)
spellingShingle Orthogonally additive holomorphic functions of bounded type over C(K)
Carando, Daniel Germán
HOLOMORPHIC FUNCTIONS OVER C(K)
INTEGRAL REPRESENTATION
ORTHOGONALLY ADDITIVE
title_short Orthogonally additive holomorphic functions of bounded type over C(K)
title_full Orthogonally additive holomorphic functions of bounded type over C(K)
title_fullStr Orthogonally additive holomorphic functions of bounded type over C(K)
title_full_unstemmed Orthogonally additive holomorphic functions of bounded type over C(K)
title_sort Orthogonally additive holomorphic functions of bounded type over C(K)
dc.creator.none.fl_str_mv Carando, Daniel Germán
Lassalle, Silvia Beatriz
Zalduendo, Ignacio Martin
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Lassalle, Silvia Beatriz
Zalduendo, Ignacio Martin
author_role author
author2 Lassalle, Silvia Beatriz
Zalduendo, Ignacio Martin
author2_role author
author
dc.subject.none.fl_str_mv HOLOMORPHIC FUNCTIONS OVER C(K)
INTEGRAL REPRESENTATION
ORTHOGONALLY ADDITIVE
topic HOLOMORPHIC FUNCTIONS OVER C(K)
INTEGRAL REPRESENTATION
ORTHOGONALLY ADDITIVE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form f(x)=∫Kh(x)dμ for some μ and holomorphic h : C (K) → L1(μ) of bounded type.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lassalle, Silvia Beatriz. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
description It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form f(x)=∫Kh(x)dμ for some μ and holomorphic h : C (K) → L1(μ) of bounded type.
publishDate 2010
dc.date.none.fl_str_mv 2010-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98725
Carando, Daniel Germán; Lassalle, Silvia Beatriz; Zalduendo, Ignacio Martin; Orthogonally additive holomorphic functions of bounded type over C(K); Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 53; 3; 10-2010; 609-618
0013-0915
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98725
identifier_str_mv Carando, Daniel Germán; Lassalle, Silvia Beatriz; Zalduendo, Ignacio Martin; Orthogonally additive holomorphic functions of bounded type over C(K); Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 53; 3; 10-2010; 609-618
0013-0915
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/orthogonally-additive-holomorphic-functions-of-bounded-type-over-ck/B9719DF1CC1E0AB4274182C32428050D
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0013091509000248
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083162417922048
score 13.22299

Publicaciones similares