Frostman and Fourier characterisations of fractal dimensions
Kenneth J. Falconer, Shuqin Zhang
TL;DR
This paper explores Frostman-type characterisations and Fourier-based criteria for various fractal dimensions, including less common ones like modified lower box and upper correlation dimensions, enhancing understanding of their properties.
Contribution
It introduces new characterisations and Fourier-based expressions for a range of fractal dimensions, including less familiar variants.
Findings
Derived properties of modified lower box dimension
Expressed fractal dimensions in terms of Fourier measures
Enhanced understanding of extremal measure criteria
Abstract
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension. We also express a number of fractal dimensions in terms of Fourier properties of measures.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Theoretical and Computational Physics · Stochastic processes and statistical mechanics