Denis Krutikov, Christian Remling
Schr\"odinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure
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ABSTRACT.  We study the POINTWISE behavior of the Fourier transform of the spectral 
measure for discrete one-dimensional Schr\"odinger 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.