Orthogonal matrix polynomials and higher order recurrence relations

Details Orthogonal matrix polynomials and higher order recurrence relations Orthogonal matrix polynomials and higher order recurrence relations

1993-10-05

arxiv.org/abs/math/9310220v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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. In this paper 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 $N\times N$ 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.

Affiliated with

Also associated with

No associations

Rating

Orthogonal matrix polynomials and higher order recurrence relations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orthogonal matrix polynomials and higher order recurrence relations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orthogonal matrix polynomials and higher order recurrence relations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-667103