@article{69e0bdba29c04e50ae07f52057b7856d,

title = "GAUSSIAN ANALYTIC FUNCTIONS OF BOUNDED MEAN OSCILLATION",

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.",

keywords = "Bloch, Gaussian analytic functions, bounded mean oscillation, function theory on the disc, probability",

author = "Alon Nishry and Elliot Paquette",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.",

year = "2023",

doi = "10.2140/apde.2023.16.89",

language = "אנגלית",

volume = "16",

pages = "89--117",

journal = "Analysis and PDE",

issn = "2157-5045",

publisher = "Mathematical Sciences Publishers",

number = "1",

}