Grassmann geometry of zero sets in reproducing kernel Hilbert spaces

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Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.

Detalles Bibliográficos
Autores principales: Andruchow, Esteban, Chiumiento, Eduardo Hernan, Varela, Alejandro
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: Academic Press Inc Elsevier Science 2024
Materias:
Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
Acceso en línea:http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1820
Aporte de:
Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento
id I71-R177-UNGS-1820
record_format dspace
spelling I71-R177-UNGS-18202024-12-23T14:30:42Z Grassmann geometry of zero sets in reproducing kernel Hilbert spaces Andruchow, Esteban Chiumiento, Eduardo Hernan Varela, Alejandro Analytic functions spaces Geodesics Grassmann manifold Hardy space Reproducing kernels Zero sets 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. 2024-12-23T14:30:42Z 2024-12-23T14:30:42Z 2021 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion 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 eng http://dx.doi.org/10.1016/j.jmaa.2021.125107 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Academic Press Inc Elsevier Science 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
institution Universidad Nacional de General Sarmiento
institution_str I-71
repository_str R-177
collection Repositorio Institucional Digital de Acceso Abierto (UNGS)
language Inglés
orig_language_str_mv eng
topic Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
spellingShingle Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
Andruchow, Esteban
Chiumiento, Eduardo Hernan
Varela, Alejandro
Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
topic_facet Analytic functions spaces
Geodesics
Grassmann manifold
Hardy space
Reproducing kernels
Zero sets
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
format Artículo
Artículo
publishedVersion
author Andruchow, Esteban
Chiumiento, Eduardo Hernan
Varela, Alejandro
author_facet Andruchow, Esteban
Chiumiento, Eduardo Hernan
Varela, Alejandro
author_sort Andruchow, Esteban
title Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
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
publisher Academic Press Inc Elsevier Science
publishDate 2024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1820
work_keys_str_mv AT andruchowesteban grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
AT chiumientoeduardohernan grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
AT varelaalejandro grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
_version_ 1824528620223201280

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