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$%S. Alkhatib and V. P. Kostov, The Schur-Szegö composition of real polynomials of degree 2,
Rev. Mat. Complut. 21 (2008), no. 1, 191–206.%$

The Schur-Szegö Composition of Real
Polynomials of Degree 2

Soliman ALKHATIB and Vladimir Petrov KOSTOV

Université de Nice

Laboratoire de Mathématiques

Parc Valrose

06108 Nice Cedex 2 — France

khatib@math.unice.fr kostov@math.unice.fr

Laboratoire de Mathématiques

Parc Valrose

06108 Nice Cedex 2 — France

khatib@math.unice.fr kostov@math.unice.fr

Accepted: September 17, 2007

ABSTRACT

A real polynomial in one real variable is hyperbolic if its roots are all real. The composition of Schur-Szegö of the polynomials and is the polynomial . In the present paper we show how for and when and are real or hyperbolic the roots of depend on the roots or the coefficients of and . We consider also the case when is arbitrary and and are of the form . This case is interesting in the context of the possibility to present every polynomial having one of its roots at as a composition of polynomials of the form .

Key words: composition of Schur-Szegö, hyperbolic polynomial.

2000 Mathematics Subject Classification: 12D10.