TWO PROBLEMS ON RANDOM ANALYTIC FUNCTIONS IN FOCK SPACES

Xiang Fang, Pham Trong Tien

Research output: Contribution to journalArticlepeer-review

Abstract

Let f(z) = Σn=0anznbe an entire function on the complex plane and let Rf(z) = Σn=0anXnznbe its randomization induced by a standard sequence (Xn)nof independent Bernoulli, Steinhaus or Gaussian random variables. In this paper, we characterize those functions f(z) such that Rf(z) is almost surely in the Fock space Fpαfor any p; α ∈ (0, ∞). Then such a characterization, together with embedding theorems which are of independent interests, is used to obtain a Littlewood-type theorem, aka regularity improvement under randomization within the scale of Fock spaces. Other results obtained in this paper include (a) a characterization of random analytic functions in the mixed norm space F(∞; q; α), an endpoint version of Fock spaces, via entropy integrals; (b) a complete description of random lacunary elements in Fock spaces; (c) a complete description of random multipliers between different Fock spaces.

Original languageEnglish
JournalCanadian Journal of Mathematics
DOIs
StateAccepted/In press - 2022

Keywords

  • Fock spaces
  • Random analytic functions

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