Log-integrability of Rademacher Fourier series, with applications to random analytic functions

Fedor Nazarov; Alon Nishry; Mikhail Sodin

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arXiv · 1301.0529

Log-integrability of Rademacher Fourier series, with applications to random analytic functions

Fedor Nazarov·Alon Nishry·Mikhail Sodin

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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.

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Fedor Nazarov, Alon Nishry, Mikhail Sodin. 2013-01-03. Log-integrability of Rademacher Fourier series, with applications to random analytic functions. https://arxiv.org/abs/1301.0529

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