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

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.