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arXiv · 1311.7386

Multifractal analysis of some inhomogeneous multinomial measures with distinct analytic Olsen's $b$ and $B$ functions

Shuang Shen
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Abstract

Inhomogeneous multinomial measures on the mixed symbolic spaces and the real line are given. By counting the zeros of the corresponding generalized Dirichlet polynomials, one obtains a probability measure whose Olsen's functions $b$ and $B$ are analytic and their graphs differ except at two points where they are tangent. Also, interpretations of the Legendre transform of $b$ and $B$ are given in terms of dimensions.

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Shuang Shen. 2013-11-28. Multifractal analysis of some inhomogeneous multinomial measures with distinct analytic Olsen's $b$ and $B$ functions. https://arxiv.org/abs/1311.7386

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