Parameters associated with bivariate Bernstein-Szego measures on the bi-circle
Jeffrey S. Geronimo, Philip Benge
TL;DR
This paper studies measures on the bi-circle, exploring recurrence relations of orthogonal polynomials and extending parameterizations for Bernstein-Szego measures on this domain.
Contribution
It derives new relations among recurrence coefficients and extends existing parameterizations for Bernstein-Szego measures on the bi-circle.
Findings
Derived new recurrence relations for orthogonal polynomials on the bi-circle.
Extended the parameterization framework for Bernstein-Szego measures.
Reviewed existing recurrence relations and introduced novel connections.
Abstract
We consider measures supported on the bi-circle and review the recurrence relations satisfied by the orthogonal polynomials associated with these measures constructed using the lexicographical or reverse lexicographical ordering. New relations are derived among these recurrence coefficients. We extend the results of [8] on a parameterization for Bernstein-Szego measures supported on the bi-circle.
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Taxonomy
TopicsMathematical functions and polynomials · Fractional Differential Equations Solutions · Advanced Numerical Analysis Techniques