April 26, 2024Canadian Journal of Mathematics

Random analytic functions with a prescribed growth rate in the unit disk

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Authors

XFXiang FangUniversity of Nebraska–Lincoln PTPham Trong Tien

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Implication

Theoretical analysis demonstrates mutual determination among function growth, Taylor coefficients, and zero sets in the unit disk, highlighting links between geometry and randomness.

Key Points

Prescribed polynomial growth rates for random analytic functions over the unit disk mutually and completely determine the asymptotic behavior of their Taylor coefficients.
Theoretical framework using auxiliary Banach spaces enables quantitative estimates, while incorporating Bernoulli, Steinhaus, and complex Gaussian random variables.
Highlights that the asymptotic distribution of zero sets is intrinsically coupled to function growth, establishing a comprehensive structural bridge in complex analysis.

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Fang et al. (2024) studied this question.

synapsesocial.com/papers/68e6d7e2b6db643587654798 https://doi.org/10.4153/s0008414x24000403

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Implication

Theoretical analysis demonstrates mutual determination among function growth, Taylor coefficients, and zero sets in the unit disk, highlighting links between geometry and randomness.

Random analytic functions with a prescribed growth rate in the unit disk

Discussion

Member takes

Implication

Key Points

Cite This Study

Random analytic functions with a prescribed growth rate in the unit disk

Discussion

Member takes

Implication

Key Points

Cite This Study

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