Stability of roots of polynomials under linear combinations of derivatives

Branko Ćurgus, Vania Mascioni

Let $T={\alpha }_{0}I+{\alpha }_{1}D+...+{\alpha }_n{D}^n$, where $D$ is the differentiation operator and ${\alpha }_0\ne 0$, and let $f$ be a square-free polynomial with large minimum root separation. We prov…