Measurably entire functions and their growth

Adi Glücksam

doi:10.1007/s11856-018-1800-3

Measurably entire functions and their growth

Adi Glücksam^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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[log^p |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[log^p |z|]) for any p < 2.

Original language	English (US)
Pages (from-to)	307-339
Number of pages	33
Journal	Israel Journal of Mathematics
Volume	229
Issue number	1
DOIs	https://doi.org/10.1007/s11856-018-1800-3
State	Published - Jan 1 2019

Funding

∗ Supported in part by ERC Advanced Grant 692616 and ISF Grant 382/15. Received January 24, 2018 and in revised form March 21, 2018

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-018-1800-3

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Measurably entire functions and their growth

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