TY - JOUR
T1 - TWO PROBLEMS ON RANDOM ANALYTIC FUNCTIONS IN FOCK SPACES
AU - Fang, Xiang
AU - Tien, Pham Trong
N1 - Publisher Copyright:
© 2022 Cambridge University Press. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Let f(z) = Σ∞n=0anznbe an entire function on the complex plane and let Rf(z) = Σ∞n=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.
AB - Let f(z) = Σ∞n=0anznbe an entire function on the complex plane and let Rf(z) = Σ∞n=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.
KW - Fock spaces
KW - Random analytic functions
UR - http://www.scopus.com/inward/record.url?scp=85134051757&partnerID=8YFLogxK
U2 - 10.4153/S0008414X22000372
DO - 10.4153/S0008414X22000372
M3 - 期刊論文
AN - SCOPUS:85134051757
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
SN - 0008-414X
ER -