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Israel Journal of Mathematics

, Volume 229, Issue 1, pp 307–339 | Cite as

Measurably entire functions and their growth

  • Adi GlücksamEmail author
Article
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Abstract

In 1997 B. Weiss introduced the notion of measurably entire functions and proved that they exist on every arbitrary free C-action defined on a standard probability space. In the same paper he asked about the minimal possible growth rate of such functions. In this work we show that for every arbitrary free C-action defined on a standard probability space there exists a measurably entire function whose growth rate does not exceed exp(exp[logp |z|]) for any p > 3. This complements a recent result by Buhovski, Glücksam, Logunov and Sodin who showed that such functions cannot have a growth rate smaller than exp(exp[logp |z|]) for any p < 2.

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References

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    L. Buhovsky, A. Glücksam, A. Logunov and M. Sodin, Translation-invariant probability measures on entire functions, Journal d’Analyse Mathématique, to appear, arXiv:1703.08101.Google Scholar
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    B. Weiss, Measurable entire functions, Annals of Numerical Mathematics 4 (1997), 599–605.MathSciNetzbMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Sackler Faculty of SciencesTel Aviv UniversityTel AvivIsrael

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