Exceptional Sets of Entire Functions of Completely Regular Growth.

Autor: Krivosheev, A. S., Krivosheeva, O. A.
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Zdroj: Mathematical Notes; Oct2024, Vol. 116 Issue 3, p651-668, 18p
Abstrakt: In this paper, we study sequences of complex numbers of refined order. Multiple terms are allowed in such sequences. We consider complex sequences with finite maximal density for a given refined order. We construct special coverings of multiple sets consisting of disks of special radii centered at the points . In particular, we construct coverings whose connected components have a relatively small diameter as well as coverings that are -sets. These coverings act as exceptional sets for entire functions of finite refined order and completely regular growth. Outside these sets, we obtain a representation of the logarithm of the modulus of an entire function. Earlier, a similar representation was obtained by B. Ya. Levin outside the exceptional set with respect to which only its existence is asserted. In contrast, in this paper we present a simple constructive construction of the exceptional set. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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