Global Bounds on Stable Polynomials

Greg Knese

doi:10.1007/s11785-018-0873-7

Global Bounds on Stable Polynomials

Greg Knese

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 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.

Original language	English
Pages (from-to)	1895-1915
Number of pages	21
Journal	Complex Analysis and Operator Theory
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s11785-018-0873-7
State	Published - Jun 1 2019

Keywords

Determinantal representation
Entire function
Stable polynomial

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10.1007/s11785-018-0873-7

Cite this

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abstract = "A classical inequality of Sz{\'a}sz bounds polynomials with no zeros in the upper half plane entirely in terms of their first few coefficients. Borcea–Br{\"a}nd{\'e}n generalized this result to several variables as a piece of their characterization of linear maps on polynomials preserving stability. In this paper, we use determinantal representations to prove Sz{\'a}sz type inequalities in two variables and then prove that one can use the two variable inequality to prove an inequality for several variables.",

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AB - 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 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.

KW - Determinantal representation

KW - Entire function

KW - Stable polynomial

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ER -

Global Bounds on Stable Polynomials

Abstract

Keywords

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