Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions

Abstract : For xed c, Prolate Spheroidal Wave Functions (PSWFs), denoted by ψ n,c , form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c. They have been largely studied and used after the seminal work of D. Slepian and his co-authors. In several applications, uniform estimates of the ψ n,c in n and c, are needed. To progress in this direction, we push forward the uniform approximation error bounds and give an explicit approximation of their values at 1 in terms of the Legendre complete elliptic integral of the rst kind. Also, we give an explicit formula for the accurate approximation the eigenvalues of the Sturm-Liouville operator associated with the PSWFs. 2010 Mathematics Subject Classication. Primary 42C10, 65L70. Secondary 41A60, 65L15.
Type de document :
Article dans une revue
Constructive Approximation, Springer Verlag, 2015, 〈10.1007/s00365-015-9295-1〉
Liste complète des métadonnées

Littérature citée [33 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01202320
Contributeur : Abderrazek Karoui <>
Soumis le : samedi 19 septembre 2015 - 18:33:27
Dernière modification le : jeudi 7 mars 2019 - 11:34:08
Document(s) archivé(s) le : mardi 29 décembre 2015 - 08:49:24

Fichier

Bonami_Karoui_Paper_Constr_App...
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Aline Bonami, Abderrazek Karoui. Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions. Constructive Approximation, Springer Verlag, 2015, 〈10.1007/s00365-015-9295-1〉. 〈hal-01202320〉

Partager

Métriques

Consultations de la notice

104

Téléchargements de fichiers

89