Convolution operators and zeros of entire functions

Cardon, David

doi:10.1090/S0002-9939-01-06351-1

Convolution operators and zeros of entire functions
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by David A. Cardon PDF

Proc. Amer. Math. Soc. 130 (2002), 1725-1734 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 convolution $(G*dF)(z)=\int _{-\infty }^{\infty } G(z-is) dF(s)$ has only real zeros.

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