Preprint
Aug 2026
Residual bounds for Schur-stable polynomials
Let $r_n$ be the infimum of \[ \frac{\lVert P'-P'(0)P\rVert_{H^2}}{\lVert P\rVert_{H^2}} \] over all degree-$n$ polynomials $P$ satisfying $P(0)=1$ whose zeros lie in the closed unit disk. We prove the quantitative residual bound \[ r_n\geq \exp\!\bigl(-(1+o(1))\sqrt n\log n\bigr) \qquad(n\to\infty). \] As an applicati...
Xiaojun Tan, Qihang Wang, Wei Huang et al.
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