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

Document Type

Presentation

Presentation Date

12-26-2016

Abstract or Description

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.

Sponsorship/Conference/Institution

Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop

Location

Hainan, China

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