ON GENERALIZED SPECTRAL FUNCTIONS, THE PARAMETRIZATION OF BLOCK HANKEL AND BLOCK JACOBI MATRICES, AND SOME ROOT LOCATION-PROBLEMS

The parametrization of a strongly regular block Hankel matrix in terms of certain block entries of an appropriately chosen sequence of block inverses is established. This leads to a new recipe for solving the g eneralized spectral problem for jacobi matrices. A generalized spectra l function is introduced and, together with the parametrization referr ed to above, is used to investigate the root location of certain ortho gonal matrix polynomials. The matrix analogues of two classical stabil ity tests are discussed.