Cardinal interpolation with polysplines on annuli

被引：17

作者：

Kounchev, O

Render, H

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

[2] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

来源：

JOURNAL OF APPROXIMATION THEORY | 2005年 / 137卷 / 01期

关键词：

cardinal splines; Schoenberg interpolation theorems; L-splines; cardinal spline interpolation; spherical harmonics; polyharmonic functions in annulus; biharmonic functions; polysplines;

D O I：

10.1016/j.jat.2005.08.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Cardinal polysplines of order p on annuli are functions in C2p-2 (R-n\vertical bar 0 vertical bar) which are piecewise poly-harmonic of order 17 such that Delta(p-l)S may have discontinuities on spheres in R-n, centered at the origin and having radii of the form e(j), j epsilon Z. The main result is an interpolation theorem for cardinal polysplines where the data are given by sufficiently smooth functions on the spheres of radius e(j) and center 0 obeying a certain growth condition in vertical bar j vertical bar. This result can be considered as an analogue of the famous interpolation theorem of Schoenberg for cardinal splines. (c) 2005 Elsevier Inc. All. rights reserved.

引用

页码：89 / 107

页数：19

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