Geodesic
On small perturbations of the set of zeros of functions of sine type
Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 79-101.

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A function of sine type means an entire function $S(z)$ of exponential type $\sigma>\nobreak0$, satisfying the condition $0$ outside some strip $|\operatorname{Im}z|\nobreak H$. With the normalization $S(0)=1$ these functions can be represented in the form \begin{equation} S(z)=\lim_{R\to\infty}\prod_{|\lambda_k|}(1-z\lambda_k^{-1}). \end{equation} Let $\widetilde S(z)$ denote the function obtained from $S(z)$ by replacing $\lambda_k$ by $\lambda_k+\psi_k$ in (1), where $\{\psi_k\}$ is a bounded sequence. In this paper necessary and sufficient conditions on $\{\psi_k\}$ are found, under which $\widetilde S(z)$ is also a function of sine type. Expressions for $\widetilde S(z)$ in terms of $S(z)$ are obtained in the case where $\psi_k=a_1\lambda_k^{-1}+\dots+a_n\lambda_k^{-n}+b_k\lambda_k^{-n}$, where $\{b_k\}\in L^p$, $p>1$. Bibliography: 9 titles. 
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B. Ya. Levin; I. V. Ostrovskii. On small perturbations of the set of zeros of functions of sine type. Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 79-101. http://geodesic.mathdoc.fr/item/IM2_1980_14_1_a4/

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[6] Levin B. Ya., “O funktsiyakh konechnoi stepeni, ogranichennykh na posledovatelnosti tochek”, Dokl. AN SSSR, 65:3 (1949), 265–268 | MR | Zbl

[7] Akhiezer N. I., Levin B. Ya., “Ob interpolirovanii tselykh transtsendentnykh funktsii konechnoi stepeni”, Zapiski fiz.-matem. fakulteta Kharkovskogo gos. un-ta i Kharkovsk. matem. ob-va, ser. 4, 23, 1952, 5–26 | MR

[8] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GTTL, M., 1956

[9] Marchenko V. A., Ostrovskii I. V., “Kharakteristika spektra operatora Khilla”, Matem. sb., 97:4 (1975), 540–606 | MR | Zbl