A version of Putinar's Positivstellensatz for cylinders

Autores
Escorcielo, Paula Micaela; Perrucci, Daniel Roberto
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type S×R with S={x¯∈Rn|g1(x¯)≥0,…,gs(x¯)≥0} such that the quadratic module generated by g1,…,gs in R[X1,…,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f∈R[X1,…,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,…,gs in R[X1,…,Xn,Y]. We also include an example to show that an additional assumption is necessary for Putinar's Positivstellensatz to hold on cylinders of this type.
Fil: Escorcielo, Paula Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DEGREE BOUNDS
PUTINAR'S POSITIVSTELLENSATZ
SUMS OF SQUARES
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:11336/136896
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A version of Putinar's Positivstellensatz for cylindersEscorcielo, Paula MicaelaPerrucci, Daniel RobertoDEGREE BOUNDSPUTINAR'S POSITIVSTELLENSATZSUMS OF SQUAREShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type S×R with S={x¯∈Rn|g1(x¯)≥0,…,gs(x¯)≥0} such that the quadratic module generated by g1,…,gs in R[X1,…,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f∈R[X1,…,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,…,gs in R[X1,…,Xn,Y]. We also include an example to show that an additional assumption is necessary for Putinar's Positivstellensatz to hold on cylinders of this type.Fil: Escorcielo, Paula Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier Science2020-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/136896Escorcielo, Paula Micaela; Perrucci, Daniel Roberto; A version of Putinar's Positivstellensatz for cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 224; 12; 5-2020; 1-170022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2020.106448info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404920301481?via%3Dihubinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1811.03586info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:21:16Zoai:ri.conicet.gov.ar:11336/136896instacron: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:34982025-09-29 10:21:16.612CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A version of Putinar's Positivstellensatz for cylinders
title A version of Putinar's Positivstellensatz for cylinders
spellingShingle A version of Putinar's Positivstellensatz for cylinders
Escorcielo, Paula Micaela
DEGREE BOUNDS
PUTINAR'S POSITIVSTELLENSATZ
SUMS OF SQUARES
title_short A version of Putinar's Positivstellensatz for cylinders
title_full A version of Putinar's Positivstellensatz for cylinders
title_fullStr A version of Putinar's Positivstellensatz for cylinders
title_full_unstemmed A version of Putinar's Positivstellensatz for cylinders
title_sort A version of Putinar's Positivstellensatz for cylinders
dc.creator.none.fl_str_mv Escorcielo, Paula Micaela
Perrucci, Daniel Roberto
author Escorcielo, Paula Micaela
author_facet Escorcielo, Paula Micaela
Perrucci, Daniel Roberto
author_role author
author2 Perrucci, Daniel Roberto
author2_role author
dc.subject.none.fl_str_mv DEGREE BOUNDS
PUTINAR'S POSITIVSTELLENSATZ
SUMS OF SQUARES
topic DEGREE BOUNDS
PUTINAR'S POSITIVSTELLENSATZ
SUMS OF SQUARES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type S×R with S={x¯∈Rn|g1(x¯)≥0,…,gs(x¯)≥0} such that the quadratic module generated by g1,…,gs in R[X1,…,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f∈R[X1,…,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,…,gs in R[X1,…,Xn,Y]. We also include an example to show that an additional assumption is necessary for Putinar's Positivstellensatz to hold on cylinders of this type.
Fil: Escorcielo, Paula Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type S×R with S={x¯∈Rn|g1(x¯)≥0,…,gs(x¯)≥0} such that the quadratic module generated by g1,…,gs in R[X1,…,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f∈R[X1,…,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,…,gs in R[X1,…,Xn,Y]. We also include an example to show that an additional assumption is necessary for Putinar's Positivstellensatz to hold on cylinders of this type.
publishDate 2020
dc.date.none.fl_str_mv 2020-05
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/11336/136896
Escorcielo, Paula Micaela; Perrucci, Daniel Roberto; A version of Putinar's Positivstellensatz for cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 224; 12; 5-2020; 1-17
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136896
identifier_str_mv Escorcielo, Paula Micaela; Perrucci, Daniel Roberto; A version of Putinar's Positivstellensatz for cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 224; 12; 5-2020; 1-17
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2020.106448
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404920301481?via%3Dihub
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1811.03586
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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
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score 13.070432

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