Abstract view
|
Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory
|
|
Published:2009-03-01
Printed: Mar 2009
Abstract
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: |
Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, Christoffel-Darboux
Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, Christoffel-Darboux
|
