Zeros of OPUC and long time asymptotics of Schur and related flows

Abstract

We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: αj (t) = (1 − |αj(t)|^2)(αj+1(t) − αj−1(t)) for α−1(t) = 1 boundary conditions and n = 0, 1, 2,..., with initial condition αj (0) 2 (−1, 1). We also provide examples with αj (0) 2 D for which α0(t) does not have a limit. The proofs depend on the solution via a direct/inverse spectral transform.

Additional details