A CHARACTERIZATION OF RANDOM ANALYTIC FUNCTIONS SATISFYING BLASCHKE-TYPE CONDITIONS

Yongjiang Duan, Xiang Fang, Na Zhan

Research output: Contribution to journalArticlepeer-review

Abstract

Let f(z) = P∞n=0 anzn ∈ H(D) be an analytic function over the unit disk in the complex plane, and let Rf be its randomization: ∞ (Rf)(z) = X anXnzn ∈ H(D), n=0 where (Xn)n0 is a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this note we characterize those f(z) ∈ H(D) such that the zero set of Rf satisfies a Blaschke-type condition almost surely: ∞ X (1 − |zn|)t < ∞, t > 1.

Original languageEnglish
JournalCanadian Mathematical Bulletin
DOIs
StateAccepted/In press - 2024

Keywords

  • Blaschke condition
  • Random analytic function
  • zero sets

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