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Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction

  Published:2011-04-06
 Printed: Sep 2011
  • Nicolae Strungaru,
    Department of Mathematical Sciences, Grant MacEwan University, Edmonton, AB, T5J 4S2
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Abstract

In this paper we characterize the positive definite measures with discrete Fourier transform. As an application we provide a characterization of pure point diffraction in locally compact Abelian groups.
Keywords: pure point diffraction, positive definite measure, Fourier transform of measures pure point diffraction, positive definite measure, Fourier transform of measures
MSC Classifications: 43A25 show english descriptions Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A25 - Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
 

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