Geodesic
Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation
Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 455-469 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions under which the reciprocal $1/L(\lambda)$ of an entire function with simple zeros $\lambda_k$ can be represented as a series of partial fractions $c_k/(\lambda-\lambda_k)$, $k=1,2,\dots$, are investigated. The possibility of such a representation is characterized, as is conventional, in terms of a particular ‘asymptotically regular’ behaviour of the function $L(\lambda)$. Applications to complete systems of exponentials on a line interval and to representative systems of exponentials in a convex domain are considered. Bibliography: 18 titles.
Keywords: entire function, series of partial fractions, representative systems of exponentials. 
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V. B. Sherstyukov. Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation. Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 455-469. http://geodesic.mathdoc.fr/item/SM_2009_200_3_a7/

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