A generalization of the one-step theorem for matrix polynomials
The authors give a new proof of Krein's theorem for orthogonal matrix polynomials based on a ``one-step'' version of the theorem. The paper consists of four sections: 1. The scalar case and the formulation of the main problem, 2. Preliminaries for the matrix case, 3. The one-step extension theorem for block Toeplitz matrices, and 4. The proof of Krein's theorem for orthogonal matrix polynomials. In Section 1 the authors study the Szegő orthogonal polynomials. The details about these polynomials and the proofs of Theorems 1.1 and 1.2, together with some references to related papers, can be found in the authors' recently published book ``Orthogonal systems and convolution operators'', Birkhäuser (2003; Zbl 1031.42021).
scientific article; zbMATH DE number 2021091