拟Ahlfors向量值测度的混合重分形密度
Mixed multifractal densities for quasi-Ahlfors vector-valued measures
摘要：
在目前的工作中，一些密度估计相关的向量值拟Ahlfors措施的混合多重分形分析框架内发展。基于拟Ahlfors的基本思想足以对向量值测度进行混合重分形分析。本文引入了多重分形测度的密度，并证明了这种密度可以用混合多重分形测度很好地估计。这样的估计导致了向量值拟Ahlfors测度的多重分形谱的精确计算。
英文摘要：
In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient to conduct a mixed multifractal analysis for vector-valued measures. In the present work, we introduced a multifractal density for finitely many measures and showed that such density may be estimated well by means of the mixed multifractal measures. Such estimation induces an exact computation of the multifractal spectrum of the vector-valued quasi-Ahlfors measure.
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