The Schur-Szegö composition of real polynomials of degree 2

• Autores: Soliman Alkhatib, Vladimir Petrov Kostov
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 21, Nº 1, 2008, págs. 191-206
• Idioma: inglés
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• Resumen

  • 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 .