Abstract
AbstractThis paper contains first steps towards a Szegö theory of orthogonal rational matrix‐valued functions on the unit circle 𝕋. Hereby we are guided by former work of Bultheel, González‐Vera, Hendriksen, and Njåstad on scalar orthogonal rational functions on the one side and by investigations of Delsarte, Genin, and Kamp on orthogonal matrix polynomials on the other side. An essential characteristic of our matricial orthogonalization procedure is marked by an intensive interplay between left and right matrix‐valued inner products generated by a nonnegative Hermitian Borel measure on the unit circle. The main feature of our approach is the distinguished role of Christoffel‐Darboux formulas. We consider pairs of rational matrix‐valued functions linked via Christoffel‐Darboux type relations as an own subject. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
