GAUSSIAN ANALYTIC FUNCTIONS OF BOUNDED MEAN OSCILLATION

Alon Nishry*, Elliot Paquette

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider random analytic functions given by a Taylor series with independent, centered complex Gaussian coefficients. We give a new sufficient condition for such a function to have bounded mean oscillation. Under a mild regularity assumption this condition is optimal. We give as a corollary a new bound for the norm of a random Gaussian Hankel matrix. Finally, we construct some exceptional Gaussian analytic functions which in particular disprove the conjecture that a random analytic function with bounded mean oscillation always has vanishing mean oscillation.

Original languageEnglish
Pages (from-to)89-117
Number of pages29
JournalAnalysis and PDE
Volume16
Issue number1
DOIs
StatePublished - 2023

Funding

FundersFunder number
European Research Council678520, 692616
United States-Israel Binational Science Foundation2018341
Israel Science Foundation1903/18

    Keywords

    • Bloch
    • Gaussian analytic functions
    • bounded mean oscillation
    • function theory on the disc
    • probability

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