Grassmann geometry of zero sets in reproducing kernel Hilbert spaces

dc.creatorAndruchow, Esteban
dc.creatorChiumiento, Eduardo Hernán
dc.creatorVarela, Alejandro
dc.date2021
dc.date2021-11-05T14:23:54Z
dc.date.accessioned2023-07-15T04:08:14Z
dc.date.available2023-07-15T04:08:14Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/127807
dc.identifierissn:0022-247X
dc.identifierissn:1096-0813
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7468389
dc.descriptionLet 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.
dc.descriptionFacultad de Ciencias Exactas
dc.formatapplication/pdf
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.subjectMatemática
dc.subjectGeodesics
dc.subjectGrassmann manifold
dc.subjectReproducing kernels
dc.subjectAnalytic functions spaces
dc.subjectZero sets
dc.subjectHardy space
dc.titleGrassmann geometry of zero sets in reproducing kernel Hilbert spaces
dc.typeArticulo
dc.typePreprint


Este ítem pertenece a la siguiente institución