24 citations · 163 across the 51 of their papers we have counts for
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Spectral Homogeneity of Discrete One-Dimensional Limit-Periodic Operators
Jake Fillman
We prove that a dense subset of limit periodic operators have spectra which are homogeneous Cantor sets in the sense of Carleson. Moreover, by using work of Egorova, our examples h…
Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices
David Damanik, Jake Fillman, Milivoje Lukic +1
We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of cocycles and establish a Johnson-type theor…
Spectral Approximation for Quasiperiodic Jacobi Operators
Charles Puelz, Mark Embree, Jake Fillman
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint…
Uniform Hyperbolicity for Szegő Cocycles and Applications to Random CMV Matrices and the Ising Model
David Damanik, Jake Fillman, Milivoje Lukic +1
We consider products of the matrices associated with the Szegő recursion from the theory of orthogonal polynomials on the unit circle and show that under suitable assumptions, thei…