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

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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. 
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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