The interpolation formula for a class of meromorphic functions

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• 作者：Enrico De Micheli^a ; ^{enrico.demicheli@cnr.it} ; Giovanni Alberto Viano^b ; ^{viano@ge.infn.it}
• 关键词：Interpolation ; Meromorphic function ; Pole recovery ; Sampling
• 刊名：Journal of Approximation Theory
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：168
• 期：Complete
• 页码：33-68
• 全文大小：614 K

文摘

In this paper we consider a class of functions () meromorphic in the half-plane , holomorphic in , continuous on , and satisfying a suitable Carlson-type asymptotic growth condition. First we prove that the position and the residue of the poles of can be obtained from the samples of taken at the positive half-integers. In particular, the positions of the poles are shown to be the roots of an algebraic equation. Then we give an interpolation formula for () that incorporates the information on the poles (i.e., position and residue) and which is proved to converge to the true function uniformly on as the number of samples tends to infinity and the error on the samples goes to zero. An illustrative numerical example of interpolation of a Runge-type function is also given.