# Stability of roots of polynomials under linear combinations of derivatives - Mathematics > Complex Variables

Abstract: Let $T=\alpha 0 I + \alpha 1 D + .+\alpha n D^n$, where $D$ is thedifferentiation operator and $\alpha 0 ot= 0$, and let $f$ be a square-freepolynomial with large minimum root separation. We prove that the roots of $Tf$are close to the roots of $f$ translated by $-\alpha 1-\alpha 0$.

Author: Branko Ćurgus, Vania Mascioni

Source: https://arxiv.org/