Translator Disclaimer
VOL. 46 | 2007 Stably hyperbolic polynomials
Vladimir Petrov Kostov

Editor(s) Jean-Paul Brasselet, Tatsuo Suwa

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 $\prod_n$. Suppose that for a real polynomial $P(x)$ of degree $n$ there exists $k \in \mathbf{N}$ and a polynomial $Q(x)$ of $\mathrm{degree} \le k-1$ such that $x^k P+Q \in \prod_{n+k}$. Denote the set of such polynomials $P$ by $\prod_n (k)$. Call the set $\prod_n (\infty) = \overline{\cup_{k=0}^{\infty} \prod_n (k)}$ the domain of stably hyperbolic polynomials of degree $n$. In the present paper we explore the geometric properties of the set $\prod_4 (\infty)$.

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

Rights: Copyright © 2007 Mathematical Society of Japan

PROCEEDINGS ARTICLE
10 PAGES


SHARE
Back to Top