Subharmonic Versions of Valiron Theorem on Entire Functions
Bulat N. Khabibullin, Farkhat B. Khabibullin
TL;DR
This paper investigates the growth behavior of entire functions by analyzing the canonical integral of Hadamard-Weierstrass, relating it to the measure's counting functions to establish growth estimates.
Contribution
It introduces new estimates connecting the growth of entire functions to the measure's counting functions, extending Valiron's theorem to subharmonic contexts.
Findings
Established bounds on growth using counting functions
Linked growth estimates to measure properties
Extended Valiron's theorem to subharmonic functions
Abstract
We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure
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Taxonomy
TopicsMeromorphic and Entire Functions · advanced mathematical theories · Mathematical Dynamics and Fractals