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10:00 am Monday, November 28, 2011 Thesis Defense: Spectral Properties of Limit-Periodic Schrödinger Operatorsby
Zheng Gan (Rice University) in HB 423- We investigate spectral properties of limit-periodic Schrödinger operators in l^2(Z). Our goal is to exhibit as rich a spectral picture as possible. We regard limit-periodic potentials as generated by continuous sampling along the orbits of a minimal translation of a procyclic group. This perspective was first proposed by Avila and further exploited by the author, which allows one to separate the base dynamics and the sampling function. Starting from this point of view, we conclude that all the spectral types (i.e. purely absolutely continuous, purely singular continuous, and pure point) can appear within the class of limit-periodic Schrödinger operators. We furthermore answer questions of the type how often a certain type of spectrum would occur and discuss the corresponding Lyapunov exponent. In the region of pure point spectrum, we exhibit the first almost periodic examples that are uniformly localized across the hull and the spectrum.
Submitted by damanik@rice.edu |