稳定多项式的整体界
Global bounds on stable polynomials
摘要：
Szász的一个经典不等式完全根据多项式的前几个系数在上半平面中限定了没有零点的多项式。Borcea-Brändén将这个结果推广到多个变量，作为他们对多项式上线性映射保持稳定性的一个刻画。本文改进了Szász原不等式，利用行列式表示证明了二元Szász型不等式，并证明了可以利用二元不等式证明多元不等式.
英文摘要：
A classical inequality of Szász bounds polynomials with no zeros in the upper half plane entirely in terms of their first few coefficients. Borcea-Brändén generalized this result to several variables as a piece of their characterization of linear maps on polynomials preserving stability. In this paper, we improve Szász's original inequality, use determinantal representations to prove Szász type inequalities in two variables, and then prove that one can use the two variable inequality to prove an inequality for several variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
