An asymptotic property of the roots of polynomials
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- by Hermann Flaschka PDF
- Proc. Amer. Math. Soc. 27 (1971), 451-456 Request permission
Abstract:
It is shown that if the imaginary parts of the roots ${\lambda _j}(s)$ of a polynomial $P(\lambda ,s),s \in {R^n}$, 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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 451-456
- MSC: Primary 35L40; Secondary 30A08
- DOI: https://doi.org/10.1090/S0002-9939-1971-0303102-5
- MathSciNet review: 0303102