Gårding's Theory of Hyperbolic Polynomials

F. Reese Harvey; H. Blaine Lawson

doi:10.1002/cpa.21443

Gårding's Theory of Hyperbolic Polynomials

F. Reese Harvey
, H. Blaine Lawson

Mathematics

Stony Brook University

Rice University

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

20 Scopus citations

Abstract

This paper presents a simple, self-contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke-Güler-Lewis-Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated "branches" are independent of the choice of hyperbolic direction.

Original language	English
Pages (from-to)	1102-1128
Number of pages	27
Journal	Communications on Pure and Applied Mathematics
Volume	66
Issue number	7
DOIs	https://doi.org/10.1002/cpa.21443
State	Published - Jul 2013

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10.1002/cpa.21443

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AB - This paper presents a simple, self-contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke-Güler-Lewis-Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated "branches" are independent of the choice of hyperbolic direction.

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Gårding's Theory of Hyperbolic Polynomials

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