This article is cited in 2 papers

Brief communications

Very Hyperbolic Polynomials

V. P. Kostov

Université de Nice Sophia Antipolis

Abstract: A real polynomial in one variable is hyperbolic if it has only real roots. A function $f$ is a primitive of order $k$ of a function $g$ if $f^{(k)}=g$. A hyperbolic polynomial is very hyperbolic if it has hyperbolic primitives of all orders. In the paper, we prove a property of the domain of very hyperbolic polynomials and describe this domain in the case of degree $4$.

Keywords: hyperbolic polynomial, very hyperbolic polynomial.

UDC: 512.622

Received: 22.10.2003

DOI: 10.4213/faa77

 English version: Functional Analysis and Its Applications, 2005, 39:3, 229–232

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