ON THE ZEROS OF SOME CONTINUOUS ANALOGS OF MATRIX ORTHOGONAL POLYNOMIALS AND A RELATED EXTENSION PROBLEM WITH NEGATIVE SQUARES

A new proof of a recent theorem of Ellis, Gohberg, and Lay, which identifies the number of roots of a ''continuous'' matrix orthogonal polynomial in the open upper halfplane with the number of negative eigenvalues of a related integral operator is presented. A related extension problem is then formulated and solved in assorted classes of functions which are analytic in the open upper half plane, apart from a finite number of poles. A discrete analogue of this extension problem is also formulated and solved. (C) 1994 John Wiley & Sons, Inc.