Measurably entire functions and their growth

Adi Glücksam*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)307-339
Number of pages33
JournalIsrael Journal of Mathematics
Volume229
Issue number1
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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