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

Conditions under which the reciprocal 1/L(λ) of an entire function with simple zeros λk can be represented as a series of partial fractions ck/(λ-λk), k=1,2,..., 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(λ). 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.