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 k∈N and a polynomial Q(x) of degree≤k−1 such that xkP+Q∈∏n+k. Denote the set of such polynomials P by ∏n(k). Call the set ∏n(∞)=¯∪∞k=0∏n(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