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4:00 pm Wednesday, February 20, 2013 Geometry-Analysis: H\"older continuity of an extended CMV matrixby Darren Ong (Rice) in HB227- Abstract: The CMV matrix is an operator on $\ell^2(\mathbb Z_+)$ that serves as a unitary analogue of the self-adjoint Jacobi matrix. It is a central tool in the study of orthogonal polynomials on the unit circle. We may extend the CMV matrix to an operator on $\ell^2(\mathbb Z)$, and this extended matrix is useful for understanding quantum random walks. We prove that power law bounds on the formal eigenvectors of the one-sided CMV matrix implies that the two-sided extension has spectral measure that is H\"older continuous, using techniques developed in the self-adjoint case by Damanik, Killip and Lenz. Our result implies spreading in the corresponding quantum random walk
Submitted by hardt@rice.edu |