Some properties of solutions of Yule-Walker type equations

The distribution of spectra of scalar and matrix polynomials generated by solutions of Yule-Walker type equations with respect to the real line and the unit circle is investigated. A description of the spectral distribution is given in terms of the inertia of the corresponding hermitian block Hankel or block Toeplitz matrix. These results can be viewed as matrix analogues of M.G. Krein's theorems on polynomials orthogonal on the unit circle. © 1992.