Linear finite difference operators preserving Laguerre-Pólya class

O. Katkova, M. Tyaglov, A. Vishnyakova

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-Pólya class of entire functions…