Mathematical Sciences: Faculty Presentations (1991-2022)

Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

Document Type

Presentation

Presentation Date

2-3-2017

Copyright

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

Sponsorship/Conference/Institution

Harmonic Analysis and Geometry of Fractal Sets (HAFS)

Location

Columbus, OH

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