On the zeros of eigenpolynomials of Hermitian Toeplitz matrices (Q484794)

This is a long article devoted to a refinement of a result by \textit{P. Delsarte} et al. [Circuits Syst. Signal Process. 3, 207--223 (1984; Zbl 0557.15009)] and \textit{P. Delsarte} and \textit{Y. Genin} [Lect. Notes Control Inf. Sci. 58, 194--213 (1984; Zbl 0559.15017)] on the number of zeros on the unit circle of eigenpolynomials of complex Hermitian matrices and generalized Carathéodory representations of such matrices. The approach here is of a geometric nature and it is based on the paper by \textit{I. Schur} [Berl. Ber. 1912, 4--15 (1912; JFM 43.0479.01)].