Matrix representations for some self-similar measures on ℝ^d

2022/01/06 by Wu, Yu-Feng
#28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.01909

Abstract

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,∞). This extends an earlier result of Feng (J. Lond. Math. Soc.(2) 68(1):102--118, 2003) to higher dimensions.

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