Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series

Krein-type theorems and ordered structure for Cauchy–de Branges spaces

“…Some further refinements of this result are due to A.G. Bakan and V.B. Sherstyukov (see, e.g., [21] and references therein).…”

“…As a corollary of Theorem 1.1 we see that if a finite order function F with zeros in a strip or a function of order less than γ −1 with zeros in the angle of size πγ admits the representation (1.2), then F is a function of exponential type. The first of these observations was proved in [21] where Krein-type theorems for functions with zeros in a strip were studied.…”

Efficient solution of parameter‐dependent quasiseparable systems and computation of meromorphic matrix functions

“…The same conclusion applies to the problem of computing the function of a quasiseparable matrix whenever the function can be represented as a series of partial fractions. The classes of meromorphic functions admitting such a representation were investigated for instance in the work of Sherstyukov . Other partial fraction approximations of certain analytic functions can be found in the work of Hale et al In the next section, we describe an effective algorithm for this task.…”

Application of Krein’s series to calculation of sums containing zeros of the Bessel functions

“…Later, representation (0.1) was termed the expansion of the function 1/L(z) in Krein's series. Questions concerning Krein's series and their applications were the subject of numerous studies (the background and the bibliography can be found in [3]). …”