De Bruijn's question on the zeros of Fourier transforms

Haseo Ki, Young One Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let f (z) be a real entire function of genus 1*, Δ ≥ 0, and suppose that for each ε > 0, all but a finite number of the zeros of f(z) lie in the strip |Im z| ≤ ≤ Δ + ε. Let λ be a positive constant such that lim supr → ∞ log M(r; f)/r2 < 1/(4λ). It is shown that for each ε > 0, all but a finite number of the zeros of the entire function e -λD2 f(z) := ∑m=0 (-λ)mf(2m)(z)/m! lie in the strip |Im z| ≤ √max{Δ2 - 2λ, 0} + ε; and if Δ 2 < 2λ, then all but a finite number of the zeros of e -λD2 f(z) are real and simple. As a consequence, de Bruijn's question whether the functions eλt2, λ > 0, are strong universal factors is answered affirmatively.

Original languageEnglish
Pages (from-to)369-387
Number of pages19
JournalJournal d'Analyse Mathematique
Volume91
DOIs
Publication statusPublished - 2003 Jan 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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