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Convolution operators and zeros of entire functions


Author: David A. Cardon
Journal: Proc. Amer. Math. Soc. 130 (2002), 1725-1734
MSC (2000): Primary 44A35, 30C15
DOI: https://doi.org/10.1090/S0002-9939-01-06351-1
Published electronically: October 17, 2001
MathSciNet review: 1887020
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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 convolution $(G*dF)(z)=\int_{-\infty}^{\infty} G(z-is)\,dF(s)$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: https://doi.org/10.1090/S0002-9939-01-06351-1
Keywords: Convolution, zeros of entire functions, Laguerre-P\'olya class
Received by editor(s): December 5, 2000
Published electronically: October 17, 2001
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2001 American Mathematical Society

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