Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups

Kluv´anek extended the Whittaker-Kotel’nikov-Shannon theorem to the abstract harmonic analysis setting over a LCA group G. 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...

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Autor principal: Medina, Juan Miguel
Formato: Artículo
Lenguaje:Inglés
Publicado: Universidad de Buenos Aires 2025
Materias:
MATEMATICA
MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
Acceso en línea:https://repositorio.uca.edu.ar/handle/123456789/20837
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Repositorio Institucional de la Universidad Católica Argentina (UCA) de Universidad Católica Argentina
id I33-R139-123456789-20837
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spelling I33-R139-123456789-208372025-11-11T05:01:39Z Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups Medina, Juan Miguel MATEMATICA MUESTREO ANALISIS ARMÓNICO ABSTRACTO Kluv´anek extended the Whittaker-Kotel’nikov-Shannon theorem to the abstract harmonic analysis setting over a LCA group G. 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. This condition was later shown to be necessary in general. 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. 2025-11-10T17:44:54Z 2025-11-10T17:44:54Z 2022 Artículo https://repositorio.uca.edu.ar/handle/123456789/20837 eng Atribución-NoComercial-CompartirIgual 4.0 Internacional http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Universidad de Buenos Aires Workshop in Harmonic Analysis, Sampling Theory, Machine Learning, and Data Science. 2022
institution Universidad Católica Argentina
institution_str I-33
repository_str R-139
collection Repositorio Institucional de la Universidad Católica Argentina (UCA)
language Inglés
topic MATEMATICA
MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
spellingShingle MATEMATICA
MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
Medina, Juan Miguel
Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
topic_facet MATEMATICA
MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
description Kluv´anek extended the Whittaker-Kotel’nikov-Shannon theorem to the abstract harmonic analysis setting over a LCA group G. 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. This condition was later shown to be necessary in general. 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.
format Artículo
author Medina, Juan Miguel
author_facet Medina, Juan Miguel
author_sort Medina, Juan Miguel
title Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
title_short Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
title_full Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
title_fullStr Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
title_full_unstemmed Laws of Large Numbers, Spectral Translates and Sampling over LCA Groups
title_sort laws of large numbers, spectral translates and sampling over lca groups
publisher Universidad de Buenos Aires
publishDate 2025
url https://repositorio.uca.edu.ar/handle/123456789/20837
work_keys_str_mv AT medinajuanmiguel lawsoflargenumbersspectraltranslatesandsamplingoverlcagroups
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