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A PDE version of the Szego case for polynomials orthogonal on the circle

Mathematical Physics & 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.