4 citations · 9 across the 6 of their papers we have counts for
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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…
Simon's OPUC Hausdorff Dimension Conjecture
David Damanik, Shuzheng Guo, Darren C. Ong
We show that the Szegő matrices, associated with Verblunsky coefficients obeying for some , are b…
Restrictions on the existence of a canonical system flow hierarchy
Injo Hur, Darren C. Ong
The KdV hierarchy is a family of evolutions on a Schrödinger operator that preserves its spectrum. Canonical systems are a generalization of Schrödinger operators, that nevertheles…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
Wencai Liu, Darren C. Ong
We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential…
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…
Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky Coefficients have generic purely singular continuous spectrum
Darren C. Ong
As an application of the Gordon lemma for orthogonal polynomials on the unit circle, we prove that for a generic set of quasiperiodic Verblunsky coefficients the corresponding two-…