Zeros of OPUC and Long Time Asymptotics of Schur and Related Flows

Details Zeros of OPUC and Long Time Asymptotics of Schur and Related Flows Zeros of OPUC and Long Time Asymptotics of Schur and Related Flows

2006-10-31

arxiv.org/abs/math/0610987v1

Mathematics

Spectral Theory

Scientific paper

We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: $\alpha_j(t)=(1- |\alpha_j(t)|^2) (\alpha_{j+1}(t)-\alpha_{j-1}(t))$ for $\alpha_{-1}(t)= 1$ boundary conditions and $n=0,1,2,...$, with initial condition $\alpha_j(0)\in (-1,1)$. We also provide examples with $\alpha_j(0)\in\mathbb{D}$ for which $\alpha_0(t)$ does not have a limit. The proofs depend on the solution via a direct/inverse spectral transform.

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