CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

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

  Published:2009-03-01
 Printed: Mar 2009
  • L. Miranian
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

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
MSC Classifications: 42C99 show english descriptions None of the above, but in this section 42C99 - None of the above, but in this section
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/