Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators

Thomas Strohmer, Tim Wertz

The almost Mathieu operator is the discrete Schrödinger operator $H_{\alpha ,\beta ,\theta }$ on ${\ell }^2(\mathbb{Z})$ defined via $(H_{\alpha ,\beta ,\theta }f)(k)=f(k+1)+f(k-1)+\beta \cos (2\pi \alpha k+\theta )f(k)$. We…