Lp extremal polynomials (0 < p < ∞) in the presence of a denumerable set of mass points-Reference-Cited by-同舟云学术

Lp extremal polynomials (0 < p < ∞) in the presence of a denumerable set of mass points

Published:2023 Issue:4 Volume:37 Page:1045-1052
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Abbassi Ahmed¹,Belhout Mohamed²

Affiliation:

1. Laboratoire de Mathématiques et Physique appliqueés, École Normale Supérieure de Bousaada, Bousaada, Algeria

2. Laboratoire ICJ, INSA de Lyon, Villeurbanne Cedex, France

Abstract

We study, for all p > 0 the asymptotic behavior of Lp extremal polynomials with respect to the measure ? = ? + ?, ? denotes a positive measure whose support is the unit circle ? plus a denumerable set of mass points, which accumulate at ? and satisfy Blaschke?s condition and ? = ?a + ?s, ?s the absolutely continuous part of the measure satisfies Szeg? condition and ?s the singular part. Our main result is the explicit strong asymptotic formulas for the Lp extremal polynomials.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference8 articles.

1. L. Geronimus, On some extremal problem in Lp σ spaces, Math. Sbornik 31 (1952), 3 − 23 (Russian).

2. H. Widom, Extremal polynomials associated with a systeme of curves and arcs in the complex plan, Adv. Math 3 (1969) 127-232.

3. V. A. Kaliaguine and R. Benzine, Sur la formule asymptotique des polynômes orthogonaux associès à une mesure concentr ee sur un contour plus une partie discrète finie, Bull. Soc. Math. Belg. Ser. B 41(1) (1989) 29-46 (French).

4. X. Li and K. Pan, Asymptotics for Lp extremal on the unit circle, J. Approx. Theory 67 (1991) 270-283.

5. V. A. Kaliaguine, On asymptotics of Lp extremals on a complex curve (0 < p < ∞), J. Approx. Theory 74 (1993) 226-236.12.