An asymptotic property of the roots of polynomials

Hermann Flaschka

doi:10.1090/S0002-9939-1971-0303102-5

An asymptotic property of the roots of polynomials

Hermann Flaschka

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	451-456
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	27
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1971-0303102-5
State	Published - Mar 1971
Externally published	Yes

Keywords

Hyperbolic polynomials
Roots of polynomials
Seidenberg-Tarski theorem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1971-0303102-5

Cite this

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AB - 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.

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KW - Roots of polynomials

KW - Seidenberg-Tarski theorem

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An asymptotic property of the roots of polynomials

Abstract

Keywords

ASJC Scopus subject areas

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