Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices

Details Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices

2006-12-14

arxiv.org/abs/math/0612400v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider bivariate polynomials orthogonal on the bicircle with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between the polynomials of different degrees. These formulas link the orthogonal polynomials constructed using the lexicographical ordering with those constructed using the reverse lexicographical ordering. Relations between the coefficients in the recurrence formulas are derived and used to give necessary and sufficient conditions for the existence of a positive linear functional. These results are then used to construct a class of two variable measures supported on the bicircle that are given by one over the magnitude squared of a stable polynomial. Applications to Fej\'er-Riesz factorization are also given

Affiliated with

Also associated with

No associations

Rating

Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices 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 Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two Variable Orthogonal Polynomials on the Bi-circle and Structured Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-476957