Matrix representations for some self-similar measures on \(\mathbb{R}^d\) (Q2152834)
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scientific article; zbMATH DE number 7555168
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Matrix representations for some self-similar measures on \(\mathbb{R}^d\) |
scientific article; zbMATH DE number 7555168 |
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Matrix representations for some self-similar measures on \(\mathbb{R}^d\) (English)
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11 July 2022
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The author considers equicontractive iterated function systems in \(\mathbb{R}^d\) satisfying the finite type condition. He finds a matrix representations of these measures and uses this representation to prove that the \(L^q\) spectrum of the measures is differentiable on \((0,\infty)\). This extends the result in [\textit{D.-J. Feng}, J. Lond. Math. Soc., II. Ser. 68, No. 1, 102--118 (2003; Zbl 1041.28004)] to higher dimensions.
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self-similar measures
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finite type condition
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matrix representations
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\(L^q\)-spectrum
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