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12:00 pm Wednesday, January 25, 2017 Spectral Theory Brown Bag Seminar: Reflectionless Discrete Schr\"odinger Operators Are Spectrally Atypical by Tom VandenBoom (Rice University) in HBH 427- We prove that, if an isospectral torus contains a discrete Schr\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense for which finite unions of nondegenerate closed intervals do not support a discrete Schr\"odinger operator. We also show that the only reflectionless discrete Schr\"odinger operators having 0, 1, or 2 spectral gaps are periodic.
Submitted by damanik@rice.edu |