Grassmann geometry of zero sets in reproducing kernel Hilbert spaces

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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 exi...

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Autores principales: Andruchow, Esteban, Chiumiento, Eduardo Hernán, Varela, Alejandro
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2021
Materias:
Matemática
Geodesics
Grassmann manifold
Reproducing kernels
Analytic functions spaces
Zero sets
Hardy space
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/127807
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-127807
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Geodesics
Grassmann manifold
Reproducing kernels
Analytic functions spaces
Zero sets
Hardy space
spellingShingle Matemática
Geodesics
Grassmann manifold
Reproducing kernels
Analytic functions spaces
Zero sets
Hardy space
Andruchow, Esteban
Chiumiento, Eduardo Hernán
Varela, Alejandro
Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
topic_facet Matemática
Geodesics
Grassmann manifold
Reproducing kernels
Analytic functions spaces
Zero sets
Hardy space
description 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.
format Articulo
Preprint
author Andruchow, Esteban
Chiumiento, Eduardo Hernán
Varela, Alejandro
author_facet Andruchow, Esteban
Chiumiento, Eduardo Hernán
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
publishDate 2021
url http://sedici.unlp.edu.ar/handle/10915/127807
work_keys_str_mv AT andruchowesteban grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
AT chiumientoeduardohernan grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
AT varelaalejandro grassmanngeometryofzerosetsinreproducingkernelhilbertspaces
bdutipo_str Repositorios
_version_ 1764820452409081856

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