Log-integrability of Rademacher Fourier series, with applications to random analytic functions
Complex Variables
2016-12-21 v1 Probability
Abstract
We prove that any power of the logarithm of 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
Cite
@article{arxiv.1301.0529,
title = {Log-integrability of Rademacher Fourier series, with applications to random analytic functions},
author = {Fedor Nazarov and Alon Nishry and Mikhail Sodin},
journal= {arXiv preprint arXiv:1301.0529},
year = {2016}
}