Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

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, under this condition, a closed formula for the spectral dimension of the Laplacian. This is a joint work with Wei Tang and Yuanyuan Xie