Properties of Discrete Analogue of the Differential Operator $\frac{d^{2m}}{d{x}^{2m}}-\frac{d^{2m-2}}{d{x}^{2m-2}}$

Abstract

In the paper properties of the discrete analogue $D_m(h\beta )$ of the differential operator $\frac{d^{2m}}{d{x}^{2m}}-\frac{d^{2m-2}}{d{x}^{2m-2}}$ are studied. It is known, that zeros of differential operator $\frac{d^{2m}}{d{x}^{2m}}-\frac{d^{2m-2}}{d{x}^{2m-2}}$ are functions $e^x$, $e^{-x}$ and $P_{2m-3}(x)$. It is proved that discrete analogue $D_m(h\beta )$ of this differential operator also have similar properties.

arXiv comment12 pages, this paper was published in Uzbek Mathematical Journal, 2004, \No4