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Spectral measures with arbitrary Hausdorff dimensions

Published 16 Dec 2014 in math.FA | (1412.4852v1)

Abstract: In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.

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