Abstract

LOPEZ NICOLAS, José Alfonso. On Stable Sampling and Interpolation in Bernstein Spaces. Rev.colomb.mat. [online]. 2022, vol.56, n.2, pp.213-239.  Epub Jan 07, 2024. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n2.108383.

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.

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