Sampling in a weighted Sobolev space

Acala, Nestor G.; Reyes, Noli N.

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

Acala, Nestor G.¹ ; Reyes, Noli N.¹

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

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

Abstract (VO)
Résumé

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 $n \to \pm \infty$ .

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 $n \to \pm \infty$ .

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 :

Acala, Nestor G. ¹ ; Reyes, Noli N. ¹

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

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     author = {Acala, Nestor G. and Reyes, Noli N.},
     title = {Sampling in a weighted {Sobolev} space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {941--944},
     year = {2012},
     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2012.10.028},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2012.10.028/}
}

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Acala, Nestor G.; Reyes, Noli N. Sampling in a weighted Sobolev space. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 941-944. doi: 10.1016/j.crma.2012.10.028

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