MAXIMAL POINTS OF STABLE AND RELATED POLYNOMIALS

We prove that any polynomial having all its roots ina closed half-plan e, whose boundary contains the origin, has either one or two maximal p oints, and only one if it has at least one root in the open half-plane . This result concerns stable polynomials as well as polynomials havin g only real roots, including real orthogonal polynomials. (C) 1998 Aca demic Press.