Grassmann geometry of zero sets in reproducing kernel Hilbert spaces

Autores
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Varela, Alejandro
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Let H be a reproducing kernel Hilbert space of functions on a set X. We study the problem of finding a minimal geodesic of the Grassmann manifold of H that joins two subspaces consisting of functions which vanish on given finite subsets of X. We establish a necessary and sufficient condition for existence and uniqueness of geodesics, and we then analyze it in examples. We discuss the relation of the geodesic distance with other known metrics when the mentioned finite subsets are singletons. We find estimates on the upper and lower eigenvalues of the unique self-adjoint operators which define the minimal geodesics, which can be made more precise when the underlying space is the Hardy space. Also for the Hardy space we discuss the existence of geodesics joining subspaces of functions vanishing on infinite subsets of the disk, and we investigate when the product of projections onto this type of subspaces is compact.
Fuente
Journal of Mathematical Analysis and Applications. Ago. 2021; 500(1): 1-31
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/500/issue/1
Materia
Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
Repositorio Institucional UNGS
Institución
Universidad Nacional de General Sarmiento
OAI Identificador
oai:repositorio.ungs.edu.ar:UNGS/1820
Acceder
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oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1820
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Grassmann geometry of zero sets in reproducing kernel Hilbert spacesAndruchow, EstebanChiumiento, Eduardo HernanVarela, AlejandroAnalytic functions spacesGeodesicsGrassmann manifoldHardy spaceReproducing kernelsZero setsFil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.Let H be a reproducing kernel Hilbert space of functions on a set X. We study the problem of finding a minimal geodesic of the Grassmann manifold of H that joins two subspaces consisting of functions which vanish on given finite subsets of X. We establish a necessary and sufficient condition for existence and uniqueness of geodesics, and we then analyze it in examples. We discuss the relation of the geodesic distance with other known metrics when the mentioned finite subsets are singletons. We find estimates on the upper and lower eigenvalues of the unique self-adjoint operators which define the minimal geodesics, which can be made more precise when the underlying space is the Hardy space. Also for the Hardy space we discuss the existence of geodesics joining subspaces of functions vanishing on infinite subsets of the disk, and we investigate when the product of projections onto this type of subspaces is compact.Academic Press Inc Elsevier Science2024-12-23T14:30:42Z2024-12-23T14:30:42Z2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfAndruchow, E., Chiumiento, E. y Varela, A. (2021). Grassmann geometry of zero sets in reproducing kernel Hilbert spaces. Journal of Mathematical Analysis and Applications, 500(1), 1-31.0022-247Xhttp://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1820Journal of Mathematical Analysis and Applications. Ago. 2021; 500(1): 1-31https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/500/issue/1reponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoenghttp://dx.doi.org/10.1016/j.jmaa.2021.125107info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-09-29T15:01:48Zoai:repositorio.ungs.edu.ar:UNGS/1820instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-09-29 15:01:48.36Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
dc.title.none.fl_str_mv Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
title Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
spellingShingle Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
Andruchow, Esteban
Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
title_short Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
title_full Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
title_fullStr Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
title_full_unstemmed Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
title_sort Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
dc.creator.none.fl_str_mv Andruchow, Esteban
Chiumiento, Eduardo Hernan
Varela, Alejandro
author Andruchow, Esteban
author_facet Andruchow, Esteban
Chiumiento, Eduardo Hernan
Varela, Alejandro
author_role author
author2 Chiumiento, Eduardo Hernan
Varela, Alejandro
author2_role author
author
dc.subject.none.fl_str_mv Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
topic Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
dc.description.none.fl_txt_mv Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Let H be a reproducing kernel Hilbert space of functions on a set X. We study the problem of finding a minimal geodesic of the Grassmann manifold of H that joins two subspaces consisting of functions which vanish on given finite subsets of X. We establish a necessary and sufficient condition for existence and uniqueness of geodesics, and we then analyze it in examples. We discuss the relation of the geodesic distance with other known metrics when the mentioned finite subsets are singletons. We find estimates on the upper and lower eigenvalues of the unique self-adjoint operators which define the minimal geodesics, which can be made more precise when the underlying space is the Hardy space. Also for the Hardy space we discuss the existence of geodesics joining subspaces of functions vanishing on infinite subsets of the disk, and we investigate when the product of projections onto this type of subspaces is compact.
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
publishDate 2021
dc.date.none.fl_str_mv 2021
2024-12-23T14:30:42Z
2024-12-23T14:30:42Z
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 Andruchow, E., Chiumiento, E. y Varela, A. (2021). Grassmann geometry of zero sets in reproducing kernel Hilbert spaces. Journal of Mathematical Analysis and Applications, 500(1), 1-31.
0022-247X
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1820
identifier_str_mv Andruchow, E., Chiumiento, E. y Varela, A. (2021). Grassmann geometry of zero sets in reproducing kernel Hilbert spaces. Journal of Mathematical Analysis and Applications, 500(1), 1-31.
0022-247X
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1820
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://dx.doi.org/10.1016/j.jmaa.2021.125107
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv Journal of Mathematical Analysis and Applications. Ago. 2021; 500(1): 1-31
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/500/issue/1
reponame:Repositorio Institucional UNGS
instname:Universidad Nacional de General Sarmiento
reponame_str Repositorio Institucional UNGS
collection Repositorio Institucional UNGS
instname_str Universidad Nacional de General Sarmiento
repository.name.fl_str_mv Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento
repository.mail.fl_str_mv ubyd@campus.ungs.edu.ar
_version_ 1844623307764137984
score 12.559606

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