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Title: Orthogonal matrix polynomials and higher-order recurrence relations
Authors: Duran, AJ ×
Van Assche, Walter #
Issue Date: 1995
Publisher: Elsevier science publ co inc
Series Title: Linear algebra and its applications vol:219 pages:261-280
Abstract: It is well known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel measure on the real line. We extend this result and show that every system of polynomials satisfying some (2N + 1)-term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are N x N matrices. We apply this result to polynomials orthogonal with respect to a discrete Sobolev inner product and other inner products in the linear space of polynomials. As an application we give a short proof of Krein's characterization of orthogonal polynomials with a spectrum having a finite number of accumulation points.
URI: 
ISSN: 0024-3795
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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