Szegő's theorem for matrix orthogonal polynomials

Authors:
Maxim Derevyagin;Olga Holtz;Sergey Khrushchev;Mikhail Tyaglov
Affiliations:
Department of Mathematics MA 3-6, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany;Department of Mathematics MA 3-6, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany and Department of Mathematics, University of California-Berkeley, 821 Evans ...;International School of Economics, Kazakh-British Technical University, Tole bi 59, 050000 Almaty, Kazakhstan;Department of Mathematics MA 3-6, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany
Venue:
Journal of Approximation Theory
Year:
2012

Citing 2
Cited 0

Matrix analysis

Matrix analysis
Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in L2: (π)*1

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szego's theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.