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.
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页码：3345 / 3368
页数：24
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