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.
Harmonic Analysis and Geometry of Fractal Sets (HAFS)
"Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians."
Mathematical Sciences Faculty Presentations.