Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure
Abstract: We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrödinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators.
In this article we exhibit some balls lying in the quasi-Fuchsian space of once punctured tori, which are maximal in the class of balls with the same centers. The centers of our maximal balls lie on the slice determined by the trace equation y = ¯ x.