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Asymptotics of the Fourier transform of
the spectral measure for Schr\"odinger operators with bounded and
unbounded sparse potentials
ABSTRACT. We study the pointwise behavior of the Fourier transform of the
spectral measure for discrete one-dimensional Schr\"odinger
operators with unbounded sparse potentials, particularly with the
potentials of the special type, which give rise to the spectra with
Hausdorff dimensionality between $1/2$ and $1$. Operators with
bounded sparse potentials are also considered.