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) = ∑n=0 anzn ∈ H(D) be an analytic function over the unit disk in the complex plane, and let R f be its randomization: ∞ (R f)(z) = ∑ anXnzn ∈ H(D), n=0 where (Xn)n≥0 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 R f satisfies a Blaschke-type condition almost surely: ∞ ∑(1 − ∣zn∣)t < ∞, t > 1. n=1.

Original languageEnglish
Pages (from-to)670-679
Number of pages10
JournalCanadian Mathematical Bulletin
Volume67
Issue number3
DOIs
StatePublished - 1 Sep 2024

Keywords

  • Blaschke condition
  • Random analytic function
  • zero sets

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