TY - JOUR

T1 - Two problems on random analytic functions in Fock spaces

AU - Fang, Xiang

AU - Tien, Pham Trong

N1 - Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society.

PY - 2023/8/8

Y1 - 2023/8/8

N2 - Let (Formula Presented) be an entire function on the complex plane, and let (Formula Presented) be its randomization induced by a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this paper, we characterize those functions such that is almost surely in the Fock space for any. Then such a characterization, together with embedding theorems which are of independent interests, is used to obtain a Littlewood-type theorem, also known as 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, an endpoint version of Fock spaces, via entropy integrals; (b) a complete description of random lacunary elements in Fock spaces; and (c) a complete description of random multipliers between different Fock spaces.

AB - Let (Formula Presented) be an entire function on the complex plane, and let (Formula Presented) be its randomization induced by a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this paper, we characterize those functions such that is almost surely in the Fock space for any. Then such a characterization, together with embedding theorems which are of independent interests, is used to obtain a Littlewood-type theorem, also known as 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, an endpoint version of Fock spaces, via entropy integrals; (b) a complete description of random lacunary elements in Fock spaces; and (c) a complete description of random multipliers between different Fock spaces.

KW - Fock spaces

KW - Random analytic functions

KW - mixed norm space

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

SN - 0008-414X

VL - 75

SP - 1176

EP - 1198

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 4

ER -