2007/01/02 by Irina Nenciu, Nenciu, Irina
Mathematics · Physics and Astronomy · #42C05 #53D17 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math-ph #math.CA #math.MP #math.SG #msc:42C05 #msc:53D17 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0701055
10 pages; the statements and proofs have been corrected and expanded, and some further comments have been added
openalex publication_date 2007/01/02 · arxiv created 2011/10/24 · arxiv updated 2011/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The connection of orthogonal polynomials on the unit circle (OPUC) to the defocusing Ablowitz-Ladik integrable system involves the definition of a Poisson structure on the space of Verblunsky coefficients. In this paper, we compute the complete set of Poisson brackets for the monic orthogonal and the orthonormal polynomials on the unit circle, as well as for the second kind polynomials and the Wall polynomials. This answers a question posed by Cantero and Simon for the case of measures with finite support. We also show that the results hold for the case of measures with periodic Verblunsky coefficients.