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The interpolation formula for a class of meromorphic functions (Articolo in rivista)

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The interpolation formula for a class of meromorphic functions (Articolo in rivista) (literal)

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De Micheli Enrico; Viano Giovanni Alberto (2013)
The interpolation formula for a class of meromorphic functions
in Journal of approximation theory (Print)
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Istituto di Biofisica, Consiglio Nazionale delle Ricerche, Genova, Italy; Dipartimento di Fisica, Universita' di Genova, Genova, Italy (literal)

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Abstract

In this paper we consider a class of functions $f(z)$ ($z\in\C$) meromorphic in the half-plane $\Real z >= 1/2$, holomorphic in {2} < \Real z < 1/2$, continuous on $\Real z = 0$, and satisfying a suitable Carlson-type asymptotic growth condition. First we prove that position and residue of the poles of $f(z)$ can be obtained from the samples of $f(z)$ 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 $f(x+1/2)$ ($x=\Real z$) that incorporates the information on the poles (i.e., position and residue) and which is proved to converge to the true function uniformly on $x >= x_0>-1/2$ 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. (literal)

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