Scholarlink

<p>The Szász inequality is a classical result that provides a bound for polynomials with zeros in the upper half of the complex plane, expressed in terms of their low-order coefficients. Generalizations of this result to polynomials in several variables have been obtained by Borcea-Brändén and Knese. In this article, we discuss the Szász inequality in the context of polynomials with matrix coefficients or matrix variables. In the latter case, the estimation provided by the Szász-type inequality can be sharper than that offered by the von Neumann inequality. As a byproduct, we improve the scalar Szász inequality by relaxing the assumption regarding the location of zeros. Finally, we estimate the Agler norm of a scalar multivariate polynomial.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Szász Inequality for Matrix Polynomials and Functional Calculus

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月4日

查看全文
  • Piotr Pikul,
  • Oskar Jakub Szymański,
  • Michał Wojtylak

摘要

The Szász inequality is a classical result that provides a bound for polynomials with zeros in the upper half of the complex plane, expressed in terms of their low-order coefficients. Generalizations of this result to polynomials in several variables have been obtained by Borcea-Brändén and Knese. In this article, we discuss the Szász inequality in the context of polynomials with matrix coefficients or matrix variables. In the latter case, the estimation provided by the Szász-type inequality can be sharper than that offered by the von Neumann inequality. As a byproduct, we improve the scalar Szász inequality by relaxing the assumption regarding the location of zeros. Finally, we estimate the Agler norm of a scalar multivariate polynomial.