On summability of weighted Lagrange interpolation. III
Authors: László Szili1; Péter Vértesi2
Source: Acta Mathematica Hungarica, Volume 104, Numbers 1-2, 2004 , pp. 39-62(24)
Publisher: Springer
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Abstract:
Starting from the Lagrange interpolation on the roots of Jacobi polynomials, a wide class of discrete linear processes is constructed using summations. Some special cases are also considered, such as the Fejér, de la Vallée Poussin, Cesàro, Riesz and Rogosinski summations. The aim of this note is to show that the sequences of this type of polynomials are uniformly convergent on the whole interval [-1,1] in suitable weighted spaces of continuous functions. Order of convergence will also be investigated. Some statements of this paper can be obtained as corollaries of our general results proved in [15].Keywords: weighted interpolation; uniform convergence; weighted approximation; Jacobi weights; summations
Document Type: Research article
DOI: 10.1023/B:AMHU.0000034361.65209.37
Affiliations: 1: Department of Numerical Analysis, Loránd Eötvös University Budapest, Pázmány P. Sétány I/C, H-1117, Hungary, Email: szili@ludens.elte.hu 2: Alfréd Rényi Institute Mathematics, Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics Budapest, Reáltanoda U. 13-15, H--1053, Hungary, Email: vertesi@renyi.hu
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