Gårding's Theory of Hyperbolic Polynomials |
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| Authors: | F Reese Harvey H Blaine Lawson JR |
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| Institution: | 1. Department of Mathematics, Rice University, Houston, TX 77251‐1892, USA;2. Department of Mathematics, Stony Brook University, Stony Brook, NY 11794‐3651, USA |
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| 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. © 2013 Wiley Periodicals, Inc. |
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