Minimax principle and lower bounds in H$^{2}$-rational approximation - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Approximation Theory Année : 2015

Minimax principle and lower bounds in H$^{2}$-rational approximation

Résumé

We derive some lower bounds in rational approximation of given degree to functions in the Hardy space $H^2$ of the disk. We apply these to asymptotic errors rates in approximation to Blaschke products and to Cauchy integrals on geodesic arcs. We also explain how to compute such bounds, either using Adamjan-Arov-Krein theory or linearized errors, and we present a couple of numerical experiments on several types of functions. We dwell on the Adamjan-Arov-Krein theory and a maximin principle developed in the article "An L^p analog of AAK theory for p >= 2", by L. Baratchart and F. Seyfert, in the Journal of Functional Analysis, 191 (1), pp. 52-122, 2012.
Fichier principal
Vignette du fichier
BCQ2013.pdf (454.84 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00922815 , version 1 (05-01-2015)
hal-00922815 , version 2 (24-03-2015)
hal-00922815 , version 3 (11-12-2015)

Identifiants

Citer

Laurent Baratchart, Sylvain Chevillard, Tao Qian. Minimax principle and lower bounds in H$^{2}$-rational approximation. Journal of Approximation Theory, 2015, ⟨10.1016/j.jat.2015.03.004⟩. ⟨hal-00922815v3⟩

Collections

INRIA INSMI INRIA2
203 Consultations
202 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More