Sampling in a weighted Sobolev space

Nestor G. Acala; Noli N. Reyes

doi:10.1016/j.crma.2012.10.028

Mathematical Analysis/Theory of Signals

Sampling in a weighted Sobolev space
[Échantillonage dans un espace de Sobolev avec poids]

Présenté par : Yves Meyer

Nestor G. Acala ¹ ; Noli N. Reyes ¹

¹ University of the Philippines – Diliman, Institute of Mathematics, Quezon City, 1101, Philippines

Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 941-944.

Résumé
Abstract

Nous démontrons que toute fonction f dans un certain espace de Sobolev avec poids est complètement determinée par un échantillon ${f (t_{n})}_{n \in Z} \cup {\hat{f} (λ_{k})}_{k \in Z}$ sur des convenables suites croissantes ${t_{n}}_{n \in Z}$ et ${λ_{n}}_{n \in Z}$ , tendant vers ±∞ lentement, quand $n \to \pm \infty$ .

We show that functions f in some weighted Sobolev space are completely determined by time-frequency samples ${f (t_{n})}_{n \in Z} \cup {\hat{f} (λ_{k})}_{k \in Z}$ along appropriate slowly increasing sequences ${t_{n}}_{n \in Z}$ and ${λ_{n}}_{n \in Z}$ tending to ±∞ as $n \to \pm \infty$ .

Reçu le : 2011-11-10
Accepté le : 2012-10-29
Publié le : 2012-11-01

DOI : 10.1016/j.crma.2012.10.028

Affiliations des auteurs :

Nestor G. Acala ¹ ; Noli N. Reyes ¹

¹ University of the Philippines – Diliman, Institute of Mathematics, Quezon City, 1101, Philippines

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     author = {Nestor G. Acala and Noli N. Reyes},
     title = {Sampling in a weighted {Sobolev} space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {941--944},
     publisher = {Elsevier},
     volume = {350},
     number = {21-22},
     year = {2012},
     doi = {10.1016/j.crma.2012.10.028},
     language = {en},
}

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Nestor G. Acala; Noli N. Reyes. Sampling in a weighted Sobolev space. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 941-944. doi : 10.1016/j.crma.2012.10.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.028/

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