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Svetlana Jitomirskaya, Yoram Last
Power Law Subordinacy and Singular Spectra I. Half Line Operators
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ABSTRACT. We present an extension of the Gilbert-Pearson theory of
subordinacy, which relates Hausdorff-dimensional spectral properties of
one-dimensional Schr\"odinger operators to the behavior of solutions of the
corresponding Schr\"odinger equation. We use this theory to analyze these
properties for concrete examples. In particular, for every $\alpha\in(0,1)$
we construct potentials for which the spectral measure is of exact dimension