Published February 2007
| Version public
Journal Article
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 Information
© 2007 American Institute of Mathematical Sciences. Received: September 2006; Revised: October 2006; Available Online: January 2007. Supported in part by NSF grant DMS-0140592 and U.S.–Israel Binational Science Foundation (BSF) Grant No. 2002068. It is a pleasure to thank Andrei Martínez-Finkelshtein, Irina Nenciu, Paul Nevai, and Vilmos Totik, and especially Leonid Golinskii for useful discussions and correspondence.Additional details
Identifiers
- Eprint ID
- 79419
- Resolver ID
- CaltechAUTHORS:20170726-115725562
Funding
- NSF
- DMS-0140592
- Binational Science Foundation (USA-Israel)
- 2002068
Dates
- Created
-
2017-07-26Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department , Physics Department