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Linear finite difference operators preserving Laguerre-Pólya class

Published 12 Aug 2016 in math.CA | (1608.03924v2)

Abstract: We completely describe all finite difference operators of the form $$ \Delta_{M_1, M_2, h}(f)(z)=M_1(z) f(z+h) + M_2(z) f(z-h) $$ preserving the Laguerre-P\'olya class of entire functions. Here $M_1$ and $M_2$ are some complex functions and $h$ is a nonzero complex number.

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