Stability of roots of polynomials under linear combinations of derivatives

Details Stability of roots of polynomials under linear combinations of derivatives Stability of roots of polynomials under linear combinations of derivatives

2008-08-28

arxiv.org/abs/0808.3972v2

Mathematics

Complex Variables

18 pages, 4 figures

Scientific paper

Let $T=\alpha_0 I + \alpha_1 D + ...+\alpha_n D^n$, where $D$ is the
differentiation operator and $\alpha_0\not= 0$, and let $f$ be a square-free
polynomial with large minimum root separation. We prove that the roots of $Tf$
are close to the roots of $f$ translated by $-\alpha_1/\alpha_0$.

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