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Gaussian analytic
functions of bounded mean oscillation
Alon Nishry and Elliot Paquette |
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Vol. 16 (2023), No. 1, 89–117
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Abstract |
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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
function theory on the disc, bounded mean oscillation,
Gaussian analytic functions, Bloch, probability
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Mathematical Subject Classification 2010
Primary: 30B20
Secondary: 30H35, 47B80
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Milestones
Received: 8 February 2020
Revised: 25 February 2021
Accepted: 4 May 2021
Published: 14 April 2023
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Authors |
| Alon Nishry | |
| School of Mathematical
Sciences Department of Pure Mathematics Tel Aviv University Tel Aviv Israel |
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| Elliot Paquette | |
| Department of Mathematics McGill University Montreal Canada |
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| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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