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arXiv · 1608.03924

Linear finite difference operators preserving Laguerre-P\'olya class

O. Katkova·M. Tyaglov·A. Vishnyakova
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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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O. Katkova, M. Tyaglov, A. Vishnyakova. 2016-08-12. Linear finite difference operators preserving Laguerre-P\'olya class. https://doi.org/10.1080/17476933.2017.1400539

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