Fourier transforms having only real zeros

Cardon, David

doi:10.1090/S0002-9939-04-07677-4

Fourier transforms having only real zeros
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by David A. Cardon PDF

Proc. Amer. Math. Soc. 133 (2005), 1349-1356 Request permission

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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