Schur flows and orthogonal polynomials on the unit circle

Details Schur flows and orthogonal polynomials on the unit circle Schur flows and orthogonal polynomials on the unit circle

2005-11-10

arxiv.org/abs/math/0511269v2

Mathematics

Classical Analysis and ODEs

17 pages, section 4 revised essentially

Scientific paper

The relation between the Toda lattices and similar nonlinear chains and orthogonal polynomials on the real line has been elaborated immensely for the last decades. We examine another system of the differential-difference equations known as the Schur flow within the framework of the theory of orthogonal polynomials on the unit circle. This system can be exhibited in equivalent form as the Lax equation, and the corresponding spectral measure undergoes a simple transformation. The general result is illustrated on the modified Bessel measures on the unit circle and the long time behavior of their Verblunsky coefficients.

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