论文标题
$ \ mathbb {r}^{d} $上的某些自相似度量的矩阵表示
Matrix representations for some self-similar measures on $\mathbb{R}^{d}$
论文作者
论文摘要
我们在$ \ mathbb {r}^d $上建立了矩阵表示，由Equictractive IFSS生成的$ \ mathbb {r}^d $满足有限类型条件。作为一个应用程序，我们证明了每种自相似度量的$ l^q $ -spectrum在$（0，\ infty）$上都是可区分的。这将冯（J.Lond。Math。Soc。（2）68（1）：102--118，2003）的早期结果扩展到了更高的维度。
We establish matrix representations for self-similar measures on $\mathbb{R}^d$ 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 $(0,\infty)$. This extends an earlier result of Feng (J. Lond. Math. Soc.(2) 68(1):102--118, 2003) to higher dimensions.
