Cardinal interpolation with periodic polysplines on strips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

Cardinal interpolation with periodic polysplines on strips

Authors:	A Bejancu OI Kounchev H Render

Affiliation:	1.Department of Mathematics, Kuwait University, PO Box 5969, Safat 13060,Kuwait;2.Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 8, 1113 Sofia,Bulgaria;3.Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa, s/n. 26004 Logro?o,Spain

Abstract:	Abstract We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we prove the existence of a unique function in $C^{2p-2}\left( \mathbb{R}^{n+1}\right)$ , polyharmonic of order p on each strip $\left( j,j+1\right) \times\mathbb{R}^{n}$ , $j\in\mathbb{Z}$ , and periodic in its last n variables, whose restriction to the parallel hyperplanes $\left\{ j\right\} \times\mathbb{R}^{n}$ , $j\in\mathbb{Z}$ , coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in $\left\vert j\right\vert$ . The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal $\mathcal{L}$ -splines. Keywords: cardinal $\mathcal{L}$ -splines, polyharmonic functions, multivariable interpolation Mathematics Subject Classification (2000): 41A05, 41A15, 41A63

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