49 citations · 130 across the 11 of their papers we have counts for
11 papers
Absolutely continuous spectrum for quasi-periodic Schrödinger operators
Helge Krueger
I prove that quasi-periodic Schrödinger operators in arbitrary dimension have some absolutely continuous spectrum.
Absolutely continuous spectrum for limit-periodic Schrödinger operators
Helge Krueger
We show that a large class of limit-periodic Schrödinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimen…
Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift
Helge Krueger
I give an example of a family of orthogonal polynomials on the unit circle with Verblunsky coefficients given by the skew-shift for which the associated measures are supported on t…
Periodic and limit-periodic discrete Schrödinger operators
Helge Krueger
The theory of discrete periodic and limit-periodic Schrödinger operators is developed. In particular, the Floquet--Bloch decomposition is discussed. Furthermore, it is shown that a…
Discontinuity of the Lyapunov Exponent
Zheng Gan, Helge Krueger
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schrödinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. W…
Optimality of log Hölder continuity of the integrated density of states
Zheng Gan, Helge Krueger
We construct examples, that log Hölder continuity of the integrated density of states cannot be improved. Our examples are limit-periodic.