Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

We observe that some self-similar measures defined by finite or infinite iterated function systems with overlaps satisfy certain “bounded measure type condition”, which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain a closed formula for the spectral dimension of the Laplacian defined by self-similar measures satisfying this condition