Poisson brackets of orthogonal polynomials

Authors:
María José Cantero;Barry Simon
Affiliations:
Department of Applied Mathematics, University of Zaragoza, 50018 Zaragoza, Spain;Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA
Venue:
Journal of Approximation Theory
Year:
2009

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Abstract

For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.