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Open Access
VOL. 46 | 2007 Stably hyperbolic polynomials
Chapter Author(s) Vladimir Petrov Kostov
Editor(s) Jean-Paul Brasselet, Tatsuo Suwa
Adv. Stud. Pure Math., 2007: 95-104 (2007) DOI: 10.2969/aspm/04610095

Abstract

A real polynomial in one real variable is hyperbolic if all its roots are real. Denote the set of monic hyperbolic polynomials of degree n by n. Suppose that for a real polynomial P(x) of degree n there exists kN and a polynomial Q(x) of degreek1 such that xkP+Qn+k. Denote the set of such polynomials P by n(k). Call the set n()=¯k=0n(k) the domain of stably hyperbolic polynomials of degree n. In the present paper we explore the geometric properties of the set 4().

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1128.12003
MathSciNet: MR2342888

Digital Object Identifier: 10.2969/aspm/04610095

Subjects:
Primary: 12D10

Keywords: (stably) hyperbolic polynomial , hyperbolicity domain , multiplicity vector

Rights: Copyright © 2007 Mathematical Society of Japan

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