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Fourier transforms having only real zeros


Author: David A. Cardon
Journal: Proc. Amer. Math. Soc. 133 (2005), 1349-1356
MSC (2000): Primary 42A38, 30C15
Published electronically: October 18, 2004
MathSciNet review: 2111941
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Abstract: Let $G(z)$ be a real entire function of order less than $2$ with only real zeros. Then we classify certain distribution functions $F$ such that the Fourier transform $H(z)=\int_{-\infty}^{\infty}G(it)e^{izt}\,dF(t)$ has only real zeros.


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Additional Information

David A. Cardon
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: cardon@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07677-4
Keywords: Fourier transform, zeros of entire functions, Laguerre-P\'olya class
Received by editor(s): September 23, 2003
Received by editor(s) in revised form: December 23, 2003
Published electronically: October 18, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.