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Two variable orthogonal polynomials on the bicircle and structured matrices
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1860/2700
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| Title: | Two variable orthogonal polynomials on the bicircle and structured matrices |
| Authors: | Geronimo, Jeffrey S.
Woerdeman, Hugo |
| Keywords: | Bivariate Orthogonal Polynomials
Positive Definite Linear Functionals
Moment Problem
Doubly Toeplitz Matrices
Recurrence Coefficients |
| Issue Date: | 2007 |
| Publisher: | Society for Industrial and Applied Mathematics |
| Citation: | Review of Scientific Instruments, 78(11): pp. 796–825. |
| Abstract: | 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. |
| URI: | http://dx.doi.org/10.1137/060662472
http://hdl.handle.net/1860/2700 |
| Appears in Collections: | Faculty Research and Publications (Mathematics)
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