Log-integrability of rademacher fourier series, with applications to random analytic functions

F. Nazarov; A. Nishry; M. Sodin

doi:https://doi.org/10.1090/S1061-0022-2014-01300-3

Log-integrability of rademacher fourier series, with applications to random analytic functions

F. Nazarov, A. Nishry, M. Sodin

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

It is proved that any power of the logarithm of a Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.

Original language	English
Pages (from-to)	467-494
Number of pages	28
Journal	St. Petersburg Mathematical Journal
Volume	25
Issue number	3
DOIs	https://doi.org/10.1090/S1061-0022-2014-01300-3
State	Published - 2014

Keywords

Random taylor series
Reduction principle

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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https://doi.org/10.1090/S1061-0022-2014-01300-3

Cite this

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title = "Log-integrability of rademacher fourier series, with applications to random analytic functions",

abstract = "It is proved that any power of the logarithm of a Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.",

keywords = "Random taylor series, Reduction principle",

author = "F. Nazarov and A. Nishry and M. Sodin",

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AU - Nazarov, F.

AU - Nishry, A.

AU - Sodin, M.

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N2 - It is proved that any power of the logarithm of a Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.

AB - It is proved that any power of the logarithm of a Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.

KW - Random taylor series

KW - Reduction principle

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DO - https://doi.org/10.1090/S1061-0022-2014-01300-3

M3 - مقالة

SN - 1061-0022

VL - 25

SP - 467

EP - 494

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

IS - 3

ER -

Log-integrability of rademacher fourier series, with applications to random analytic functions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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