Gårding's Theory of Hyperbolic Polynomials | Zendy

Harvey F. Reese | Zendy; Lawson H. Blaine | Zendy

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Gårding's Theory of Hyperbolic Polynomials

Author(s) -

Harvey F. Reese,

Lawson H. Blaine

Publication year - 2013

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21443

Subject(s) - mathematics , pointwise , convexity , simple (philosophy) , eigenvalues and eigenvectors , pure mathematics , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , financial economics , economics

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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