Irina Nenciu
Published 2004-12-14Version 1
Nenciu and Simon found that the analogue of the Toda system in the context of orthogonal polynomials on the unit circle is the defocusing Ablowitz-Ladik system. In this paper we use the CMV and extended CMV matrices, respectively, to construct Lax pair representations for this system in the periodic, finite, and infinite cases.
Spectral quantization of discrete random walks on half-line, and orthogonal polynomials on the unit circle
Confluent chains of DBT: enlarged shape invariance and new orthogonal polynomials
Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and $N$-recurrences for averages over U(N) -- \PVI $τ$-functions
