TY - JOUR

T1 - An asymptotic property of the roots of polynomials

AU - Flaschka, Hermann

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1971/3

Y1 - 1971/3

N2 - 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.

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.

KW - Hyperbolic polynomials

KW - Roots of polynomials

KW - Seidenberg-Tarski theorem

UR - http://www.scopus.com/inward/record.url?scp=84968486935&partnerID=8YFLogxK

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U2 - 10.1090/S0002-9939-1971-0303102-5

DO - 10.1090/S0002-9939-1971-0303102-5

M3 - Article

AN - SCOPUS:84968486935

VL - 27

SP - 451

EP - 456

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -