Abstract
For entire functions of order zero we introduce a new concept of regularity of growth, which is shown to possess properties similar to those which characterize the concept of totally regular growth of entire functions of finite order in the sense of Levin-Pflüger.
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B. Ya. Levin,The Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow (1956).
A. A. Gol'dberg and I. V. Ostrovskii, “On the derivatives and primitives of entire functions of totally regular growth,” in:Function Theory, Functional Analysis, and Their Applications, No. 18, 70–81 (1973).
A. A. Gol'dberg and N. V. Zabolotskii, “The concentration index of a subharmonic function of order zero,”Mat. Zametki [Math. Notes],34, No. 2, 227–236 (1983).
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Translated fromMatematicheskie Zameiki, Vol. 63, No. 2, pp. 196–208, February, 1998.
This research was partially supported by the International Science Foundation under grant No. UCR000.
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Zabolotskii, N.V. Strongly regular growth of entire functions of order zero. Math Notes 63, 172–182 (1998). https://doi.org/10.1007/BF02308756
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DOI: https://doi.org/10.1007/BF02308756