An extremal problem for a class of entire functions

Alexandre Eremenko, Peter Yuditskii

Research output: Contribution to journalArticlepeer-review

Abstract

Let f be an entire function of the exponential type, such that the indicator diagram is in [- i σ, i σ], σ > 0. Then the upper density of f is bounded by cσ, where c ≈ 1.508879 is the unique solution of the equationlog (sqrt(c2 + 1) + c) = sqrt(1 + c-2) . This bound is optimal. To cite this article: A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original languageEnglish
Pages (from-to)825-828
Number of pages4
JournalComptes Rendus Mathematique
Volume346
Issue number15-16
DOIs
StatePublished - Aug 2008
Externally publishedYes

Bibliographical note

Funding Information:
E-mail addresses: eremenko@math.purdue.edu (A. Eremenko), Petro.Yudytskiy@jku.at (P. Yuditskii). 1 Supported by NSF grant DMS-0555279. 2 Supported by Austrian Fund FWF P20413-N18.

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