Hof A.
On scaling in relation to singular spectra
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ABSTRACT. This paper relates uniform $\alpha$-H\"older continuity,
or $\alpha$-dimensionality, of spectral measures in an arbitrary
interval to the Fourier transform of the measure.
This is used to show that scaling exponents of exponential sums
obtained from time series give local upper bounds on the degree
of H\"older continuity of the power spectrum of the series.
The results have applications to generalized random walk,
numerical detection of singular continuous spectra and to the
energy growth in driven oscillators.