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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.2 Bogotá jul./dez. 2022 Epub 07-Jan-2024
https://doi.org/10.15446/recolma.v56n2.108383
Original articles
On Stable Sampling and Interpolation in Bernstein Spaces
Muestreo e Interpolación Estables en Espacios de Bernstein
1 Consejería de Educación, Cultura y Universidades de la Región de Murcia, Murcia, Spain
We define the concepts of stable sampling set, interpolation set, uniqueness set and complete interpolation set for a quasinormed space of functions and apply these concepts to Paley-Wiener spaces and Bernstein spaces. We obtain a sufficient condition on a uniformly discrete set to be an interpolation set based on a lemma of convergence of series in Paley-Wiener spaces. We also obtain a result of transference, Kadec type, of the property of being a stable sampling set, from a set with this property to other uniformly discrete set, which we apply to Bernstein spaces.
Keywords: Quasinormed spaces; stable sampling set; interpolation set; Paley-Wiener spaces; Bernstein spaces
Definimos los conceptos de conjunto de muestreo estable, conjunto de interpolación, conjunto de unicidad y conjunto de interpolación completa para los espacios quasinormados de funciones, y aplicamos estos conceptos a los espacios de Paley-Wiener y a los espacios de Bernstein. También obtenemos una condición suficiente para saber cuando un conjunto uniformemente discreto es un conjunto de interpolación, estando basada esta condición en un lema de convergencia de series en espacios de Paley-Wiener. Además, obtenemos un resultado de transferencia, tipo Kadec, sobre la propiedad de ser un conjunto de muestreo estable, de un conjunto que tiene esta propiedad a otro cunjunto que sea uniformemente discreto, y aplicamos este resultado a los espacios de Bernstein.
Palabras clave: Espacios quasinormados; conjunto de muestreo estable; conjunto de interpolación; espacios de Paley-Wiener; espacios de Bernstein
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Received: March 06, 2021; Accepted: January 06, 2023
This is an open-access article distributed under the terms of the Creative Commons Attribution License
