Phase conditions for Schur polynomials

摘要

The rate of change of phase of a real or complex Schur polynomial, evaluated along the unit circle traversed counterclockwise, is strictly positive. For polynomials with real coefficients, this bound can be tightened. These and some other fundamental bounds on the rate of change of phase are derived here, using the Tchebyshev representation of the image of a real polynomial evaluated on the unit circle.