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Computational Methods and Function Theory

, Volume 2, Issue 2, pp 449–467 | Cite as

A Generalization of Newman’s Result on the Zeros of Fourier Transforms

  • Haseo Ki
  • Young-One Kim
Article
  • 27 Downloads

Abstract

In this paper, the class of complex Borel measures μ, satisfying μ(−E) = μ(E) for every Borel set E ⊂ ℝ, such that the functions f μ,λ, λ > 0, defined by
$$f_{\mu,\lambda}(z)=\int_{-\infty}^{\infty}{\rm exp}(-{\lambda\over 2} t^2 + izt)\ d\mu(t)$$
, have only real zeros, is completely determined. It is done by establishing a general theorem (Theorem 1.3) on the asymptotic behavior of the zero-distribution of f μλ} for λ → ∞. The theorem is applied to the Riemann ξ-function.

Keywords

Zeros of Fourier transforms Riemann’s xi-function 

2000 MSC

30C15 30D10 

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Copyright information

© Heldermann  Verlag 2002

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulKorea
  2. 2.School of Mathematical SciencesSeoul National UniversitySeoulKorea

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