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

Abstract

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

Locations

• Inverse Problems and Imaging - View
• arXiv (Cornell University) - View - PDF