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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fourier transforms and the Hermite-Biehler theorem


Authors: G. Csordas and R. S. Varga
Journal: Proc. Amer. Math. Soc. 107 (1989), 645-652
MSC: Primary 30C15; Secondary 30D15, 33A70, 42A38
DOI: https://doi.org/10.1090/S0002-9939-1989-0982401-1
MathSciNet review: 982401
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Abstract: A new necessary and sufficient condition for real entire functions, represented by Fourier transforms, to have only real zeros is proved. An application of this result to the Riemann $ \xi $-function is also given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0982401-1
Keywords: Fourier transforms, Laguerre-Pólya class, Laguerre inequalities, Hermite-Biehler theorem, Riemann Hypothesis, Riemann $ \xi $-function
Article copyright: © Copyright 1989 American Mathematical Society