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dc.contributor.author
Medina, Juan Miguel
dc.date.available
2023-08-01T15:50:57Z
dc.date.issued
2022
dc.identifier.citation
Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups; Workshop in Harmonic Analysis, Sampling Theory, Machine Learning, and Data Science; Buenos Aites; Argentina; 2022; 18-19
dc.identifier.uri
http://hdl.handle.net/11336/206361
dc.description.abstract
Kluv´anek extended the Whittaker.Kotel’nikov-Shannon theorem to the abstract harmonic analysis setting over a LCA group G [5]. In this context, the classical condition for f ∈ L 2 (R) to be band limited is replaced by fb having its support essentially contained in a transversal set of a compact quotient group. Later it was proved that, in general, this condition is also necessary [1, 2,3]. Moreover, the classical interpolation formula is also equivalent to a Plancherel like isometric formula involving the L 2 (G) norm of f and the norm of the sequence of its samples over a subgroup H. Here, recalling some Laws of Large Numbers, we will prove an equivalent result for the support of the spectral measure µX of a Gaussian stationary random process X, indexed over a LCA group G. The conditions are formulated in terms of an almost sure isometric formula involving the sample variances of X, and its samples over a subgroup H respectively. The present result, partially relies on the techniques introduced recently in [4] for the study of the equivalence between the notions of AP-frame and L 2 (R)-frame.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Universidad de Buenos Aires
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Sampling
dc.subject
LCA Groups
dc.subject.classification
Matemática Aplicada
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
dc.type
info:eu-repo/semantics/publishedVersion
dc.type
info:eu-repo/semantics/conferenceObject
dc.type
info:ar-repo/semantics/documento de conferencia
dc.date.updated
2023-06-16T17:59:51Z
dc.journal.pagination
18-19
dc.journal.pais
Argentina
dc.journal.ciudad
Buenos Aires
dc.description.fil
Fil: Medina, Juan Miguel. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.union-matematica.org.ar/archivo/2022/09/07/workshop-in-harmonic-analysis-sampling-theory-machine-learning-and-data-science/
dc.conicet.rol
Autor
dc.coverage
Internacional
dc.type.subtype
Workshop
dc.description.nombreEvento
Workshop in Harmonic Analysis, Sampling Theory, Machine Learning, and Data Science
dc.date.evento
2022-11-21
dc.description.ciudadEvento
Buenos Aites
dc.description.paisEvento
Argentina
dc.type.publicacion
Journal
dc.description.institucionOrganizadora
Universidad de Buenos Aires
dc.source.revista
Workshop in Harmonic Analysis, Sampling Theory, Machine Learning, and Data Science
dc.date.eventoHasta
2022-11-25
dc.type
Workshop
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