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


Authors: F. Nazarov, A. Nishry and M. Sodin
Original publication: Algebra i Analiz, tom 25 (2013), nomer 3.
Journal: St. Petersburg Math. J. 25 (2014), 467-494
MSC (2010): Primary 42A61
DOI: https://doi.org/10.1090/S1061-0022-2014-01300-3
Published electronically: May 16, 2014
MathSciNet review: 3184602
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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.


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Additional Information

F. Nazarov
Affiliation: Department of Mathematical Sciences, Kent State University, Kent Ohio 44242
Email: nazarov@math.kent.edu

A. Nishry
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email: alonnish@post.tau.ac.il

M. Sodin
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email: sodin@post.tau.ac.il

DOI: https://doi.org/10.1090/S1061-0022-2014-01300-3
Keywords: Random Taylor series, reduction principle
Received by editor(s): January 4, 2013
Published electronically: May 16, 2014
Additional Notes: Partially supported by grant No. 2006136 of the United States–Israel Binational Science Foundation (F.N., A.N., M.S.), by U.S. National Science Foundation Grant DMS-0800243 (F.N.), and by grant No. 166/11 of the Israel Science Foundation of the Israel Academy of Sciences and Humanities (A.N., M.S.)
Dedicated: To Boris Mikhaĭlovich Makarov, on the occasion of his 80th birthday
Article copyright: © Copyright 2014 American Mathematical Society