An asymptotic property of the roots of polynomials

Research output: Contribution to journalArticle

Abstract

It is shown that if the imaginary parts of the roots λi(s) of a polynomial P(λ, s), s∈Rn, are unbounded for large |s|, then they are in fact unbounded along a one-parameter algebraic curve s=s(R). The result may be used to reduce certain questions about polynomials in several variables to an essentially one-dimensional form; this is illustrated by an application to hyperbolic polynomials.

Original languageEnglish (US)
Pages (from-to)451-456
Number of pages6
JournalProceedings of the American Mathematical Society
Volume27
Issue number3
DOIs
StatePublished - 1971
Externally publishedYes

Keywords

  • Hyperbolic polynomials
  • Roots of polynomials
  • Seidenberg-Tarski theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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