35 citations · 68 across the 13 of their papers we have counts for
7 papers · 1 filter
On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling
Michael Goldstein, Wilhelm Schlag, Mircea Voda
We study multi-frequency quasiperiodic Schrödinger operators on . We prove that for a large real analytic potential satisfying certain restrictions the spectrum consis…
On localization and the spectrum of multi-frequency quasi-periodic operators
Michael Goldstein, Wilhelm Schlag, Mircea Voda
We study multi-frequency quasi-periodic Schrödinger operators on in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's…
Homogeneity of the spectrum for quasi-periodic Schrödinger operators
Michael Goldstein, David Damanik, Wilhelm Schlag +1
We consider the one-dimensional discrete Schrödinger operator , with real-ana…
A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation
David Damanik, Michael Goldstein, Milivoje Lukic
We present an abstract multiscale analysis scheme for matrix functions , where is an Abelian group equipped with a dist…
The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations
David Damanik, Michael Goldstein, Milivoje Lukic
We study the quasi-periodic Schrödinger operator in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^ν}c(m)\exp (2πi mω…
The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous
David Damanik, Michael Goldstein, Milivoje Lukic
We consider the quasi-periodic Schrödinger operator in , where the potential is given by $$ V(x) = \sum_{m \in \mathbb{Z}^ν\set…
On the Inverse Spectral Problem for the Quasi-Periodic Schrödinger Equation
David Damanik, Michael Goldstein
We study the quasi-periodic Schrödinger equation $$ -ψ"(x) + V(x) ψ(x) = E ψ(x), \qquad x \in \IR $$ in the regime of "small" . Let , $m \in \zv$, be the standard l…