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- Chinese Academy of SciencesCN24 papers
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- University of Chinese Academy of SciencesCN13 papers
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9 papers · 1 filter
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…
Subordinacy Theory for Extended CMV Matrices
Shuzheng Guo, David Damanik, Darren C. Ong
We develop subordinacy theory for extended CMV matrices. That is, we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure as…
Generic Spectral Results for CMV Matrices with Dynamically Defined Verblunsky Coefficients
Licheng Fang, David Damanik, Shuzheng Guo
We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We…
Zero Measure and Singular Continuous Spectra for Quantum Graphs
David Damanik, Licheng Fang, Selim Sukhtaiev
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial sin…
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Valmir Bucaj, David Damanik, Jake Fillman +4
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is m…
A formula related to CMV matrices and Szego cocycles
Fengpeng Wang
For Schrodinger operators, there is a well known and widely used formula connecting the transfer matrices and Dirichlet determinants. No analog of this formula was previously know…