On summability of weighted Lagrange interpolation. II

László Szili; Péter Vértesi

doi:10.1023/b:amhu.0000028233.68543.40

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Acta Mathematica Hungarica

Volume/Issue:: Volume 103: Issue 1-2

On summability of weighted Lagrange interpolation. II

Authors:

László Szili

László Szili Loránd Eötvös University Department Of Numerical Analysis H-1117 Budapest Pázmány P. Sétány I/C H-1117 Budapest Pázmány P. Sétány I/C

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Péter Vértesi

Péter Vértesi Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics Alfréd Rényi Institute of Mathematics H-1053 Budapest Reáltanoda U. 13--15 H-1053 Budapest Reáltanoda U. 13--15

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Pages:: 1–17

Online Publication Date:: 02 Nov 2004

Publication Date:: 01 Apr 2004

Article Category:: Research Article

DOI:: https://doi.org/10.1023/b:amhu.0000028233.68543.40

Keywords:: uniform convergence; Freud-type weights; weighted approximation; weighted interpolation; summations

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Abstract

The aim of this paper is to continue our investigations started in [15], where we studied the summability of weighted Lagrange interpolation on the roots of orthogonal polynomials with respect to a weight function w. Starting from the Lagrange interpolation polynomials we constructed a wide class of discrete processes which are uniformly convergent in a suitable Banach space (C_ρ, ‖‖_ρ) of continuous functions (ρ denotes (another) weight). In [15] we formulated several conditions with respect to w, ρ, (C_ρ, ‖‖_ρ) and to summation methods for which the uniform convergence holds. The goal of this part is to study the special case when w and ρ are Freud-type weights. We shall show that the conditions of results of [15] hold in this case. The order of convergence will also be considered.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)