Minimal degree univariate piecewise polynomials with prescribed Sobolev regularity

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Al-Rashdan, Amal¹  Johnson, Michael J.¹ 

[1] Kuwait Univ, Dept Math, Safat 13060, Kuwait

关键词: Positive definite function;    Compactly supported;    B-spline;   

DOI  :  10.1016/j.jat.2011.09.008

来源: Elsevier

【 摘 要 】

For k is an element of {1, 2, 3, ... }, we construct an even compactly supported piecewise polynomial psi(k) whose Fourier transform satisfies A(k) (1 + omega(2))(-k) <= (psi) over cap (k)(omega) <= B(k)(1 + omega(2))(-k), omega is an element of R, for some constants B(k) >= A(k) > 0. The degree of psi(k) is shown to be minimal, and is strictly less than that of Wendland's function phi(1,k-1) when k > 2. This shows that, for k > 2, Wendland's piecewise polynomial phi(1,k-1) is not of minimal degree if one places no restrictions on the number of pieces. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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