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SMOOTHNESS OF THE $L^{\lowercase{q}}$-SPECTRUM OF SELF-SIMILAR MEASURES WITH OVERLAPS

Published online by Cambridge University Press:  08 August 2003

DE-JUN FENG
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China e-mail: [email protected]
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Abstract

Let $\mu$ be the self-similar measure for a linear function system $S_jx=\rho x+b_j$ ($j=1,2,\ldots,m$) on the real line with the probability weight $\{p_j\}_{j=1}^m$. Under the condition that $\{S_j\}_{j=1}^m$ satisfies the finite type condition, the $L^q$-spectrum $\tau(q)$ of $\mu$ is shown to be differentiable on $(0,\infty)$; as an application, $\mu$ is exact dimensional and satisfies the multifractal formalism.

Type
Notes and Papers
Copyright
The London Mathematical Society 2003

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