On polyharmonic interpolation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:331

Article

Haussmann, Werner ; Kounchev, Ognyan

关键词: polyharmonic functions;    multivariate interpolation;   

DOI  :  10.1016/j.jmaa.2006.09.038

来源: Elsevier

【 摘 要 】

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C-infinity or analytic functions in the ball B-R. We prove two main results on the interpolation of C-infinity or analytic functions f in the ball B-R by polyharmonic functions h of a given order of polyharmonicity p. (c) 2006 Elsevier Inc. All rights reserved.

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