Matrix representations for some self-similar measures on Rd

被引：0

作者：

Wu, Yu-Feng ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 04期

关键词：

Self-similar measures; Finite type condition; Matrix representations; L-q-spectrum; L-Q-SPECTRUM; LOCAL DIMENSIONS; FINITE-TYPE; ABSENCE;

D O I：

10.1007/s00209-022-03019-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish matrix representations for self-similar measures on R-d generated by equicontractive IFSs satisfying the finite type condition. As an application, we prove that the L-q-spectrum of every such self-similar measure is differentiable on (0, infinity). This extends an earlier result of Feng (J. Lond. Math. Soc. 68(1):102-118, 2003) to higher dimensions.

引用

页码：3345 / 3368

页数：24

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