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Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory

Published online by Cambridge University Press:  20 November 2018

L. Miranian
L. Miranian*
Affiliation:
Department of Mathematics, University of California, Berkeley CA, 94720 e-mail: luiza@math.berkeley.edu
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Abstract

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In the work presented below the classical subject of orthogonal polynomials on the unit circle is discussed in the matrix setting. An explicit matrix representation of the matrix valued orthogonal polynomials in terms of the moments of the measure is presented. Classical recurrence relations are revisited using the matrix representation of the polynomials. The matrix expressions for the kernel polynomials and the Christoffel–Darboux formulas are presented for the first time.

Keywords

42C99Matrix valued orthogonal polynomialsunit circleSchur complementsrecurrence relationskernel polynomialsChristoffel-Darboux
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 95 - 104
Copyright
Copyright © Canadian Mathematical Society 2009

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