Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces

Authors:

Affiliation:

(1) Division of Applied Mathematics, KAIST, 305-701 Taejon, Korea;(2) Department of Mathematics, University of Central Florida, 32816 Orlando, FL, USA

Abstract:

We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space W^N,2([0, ∞); e^−x) and the Sobolev-Legendre space W^N,2([−1, 1]) with respect to the Sobolev-Laguerre inner product

$varphi (f,g): = sumlimits_{k = 0}^{N - 1} {a_k } int_0^infty {f^{(k)} (x)g^{(k)} (x)e^{ - x} dx + gamma } int_0^infty {f^{(N)} (x)g^{(N)} (x)e^{ - x} dx}$

and with respect to the Sobolev-Legendre inner product

$varphi _1 (f,g): = sumlimits_{k = 0}^{N - 1} {a_k } int_{ - 1}^1 {f^{(k)} (x)g^{(k)} (x)dx + gamma } int_{ - 1}^1 {f^{(N)} (x)g^{(N)} (x)dx,}$

respectively, where a₀ = 1, a_k ≥0, 1 ≤k ≤N −1, γ > 0, and N ≥1 is an integer.

Keywords:

AMS classification 41A10 42C15

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏