Title

Best Polynomial Approximation In Sobolev-Laguerre And Sobolev-Legendre Spaces

Keywords

Best polynomial approximation; Orthogonal polynomials

Abstract

We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space WN,2([0, ∞); e-x) and the Sobolev-Legendre space WN,2([-1, 1]) with respect to the Sobolev-Laguerre inner product φ(f, g) := ∑k=0N-1ak ∫0∞ f(k)(x)g(k)(x)e-xdx + γ ∫0∞ f(N)(x)g(N)(x)e-xdx and with respect to the Sobolev-Legendre inner product φ1(f, g) := ∑k=0N-1ak ∫-11 f(k)(x)g(k)(x)dx + γ ∫-11 f(N)(x)g(N)(x)dx respectively, where a0 = 1, ak ≥ 0, 1 ≤ k ≤ N - 1, γ > 0, and N ≥ l is an integer.

Publication Date

12-1-2002

Publication Title

Constructive Approximation

Volume

18

Issue

4

Number of Pages

551-568

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-001-0022-8

Socpus ID

0035982985 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0035982985

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