Geodesic
On Some Criteria
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 119-130

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This paper sharpens the author's previous results concerning the completely regular growth of an entire function of exponential type all of whose zeros are simple, forming a sequence $\Lambda=\{\lambda_k\}_{k=1}^\infty$. For a function with real zeros, we write the growth regularity conditions (on the real axis and on the entire plane) in terms of lower bounds only for the absolute value of the derivative at the points $\lambda_k$. We also obtain an analog of Krein's theorem concerning the functions whose inverse can be expanded in the corresponding series of simple fractions.
Keywords: entire function of exponential type, completely regular growth, series of exponentials, Leont'ev problem, function with simple real zeros. 
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     author = {V. B. Sherstyukov},
     title = {On {Some} {Criteria}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {119--130},
     publisher = {mathdoc},
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     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a14/}
}
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V. B. Sherstyukov. On Some Criteria. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 119-130. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a14/