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 language | English |
---|---|
Pages (from-to) | 670-679 |
Number of pages | 10 |
Journal | Canadian Mathematical Bulletin |
Volume | 67 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2024 |
Keywords
- Blaschke condition
- Random analytic function
- zero sets