This article is cited in 3 papers

Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation

V. B. Sherstyukov

Moscow Engineering Physics Institute (National Nuclear Research University)

Abstract: 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.

UDC: 517.547.2

MSC: Primary 30D20; Secondary 30B99

Received: 12.11.2007 and 31.07.2008

DOI: 10.4213/sm4034

 English version: Sbornik: Mathematics, 2009, 200:3, 455–469

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