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math.SP2020
On Simon's Hausdorff Dimension Conjecture
David Damanik, Jake Fillman, Shuzheng Guo +1
Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients obeying for…
math.SP2018★ 3 cited
Generalized Toda flows
Darren C. Ong, Christian Remling
The classical hierarchy of Toda flows can be thought of as an action of the (abelian) group of polynomials on Jacobi matrices. We present a generalization of this to the larger gro…
math.SP2016★ 2 cited
Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks
Jake Fillman, Darren C. Ong
We show that a generic element of a space of limit-periodic CMV operators has zero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for the density of states meas…