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.
Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop
"Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities."
Mathematical Sciences Faculty Presentations.