Uniqueness of best φ-approximation from the set of splines with infinitely many simple knots

JOURNAL OF APPROXIMATION THEORY

卷:126

Article

Damas, A ; Marano, M

关键词: property A;    splines with infinitely many simple knots;    weak Chebyshev spaces;    uniqueness of best phi-approximation;   

DOI  :  10.1016/j.jat.2003.12.004

来源: Elsevier

【 摘 要 】

Let J be an open interval and denote by S-Pi the set of all the splines of degree at most n - 1 with simple knots in Pi, a countably infinite set of points in J, n greater than or equal to 2. In this paper, we prove that there exists a unique best phi-approximation to a continuous function in L-phi(J) from S-Pi, where phi : [0, infinity) --> [0, infinity) is a convex function that generalizes the pth-power functions, p greater than or equal to 1. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free