Log-integrability of Rademacher Fourier series, with applications to random analytic functions
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- by F. Nazarov, A. Nishry and M. Sodin
- St. Petersburg Math. J. 25 (2014), 467-494
- DOI: https://doi.org/10.1090/S1061-0022-2014-01300-3
- Published electronically: May 16, 2014
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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.References
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Bibliographic Information
- F. Nazarov
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent Ohio 44242
- MR Author ID: 233855
- 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
- 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.)
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 467-494
- MSC (2010): Primary 42A61
- DOI: https://doi.org/10.1090/S1061-0022-2014-01300-3
- MathSciNet review: 3184602
Dedicated: To Boris Mikhaĭlovich Makarov, on the occasion of his 80th birthday