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A PDE version of the Szego case for polynomials orthogonal on the circle
Probability| Speaker: | Serguei Dennisov, Caltech |
| Location: | 693 Kerr |
| Start time: | Tue, Oct 14 2003, 3:10PM |
For the Dirac operator in dimension three with long-range potential, we prove that the absolutely continuous spectrum fills the whole real line. The condition on the decay of the potential is optimal in some sense. For Dirac operator, this result solves one of Simon's open problems originally posed for Schrodinger equation. The proof is based on certain general principle which is especially transparent for the matrix-valued polynomials orthogonal on the circle.