Mathematical Sciences: Faculty Presentations (1991-2022)

Spectral Asymptotics of Some One-Dimensional Fractal Laplacians

Document Type

Presentation

Presentation Date

10-7-2017

Copyright

This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.

Abstract or Description

The spectral dimension of the Laplacian defined by a measure has been shown to be closely related to heat kernel estimates, which under suitable conditions determine whether wave propagates with finite or infinite speed. We observe that some self-similar measures defined by finite or infinite iterated function systems with overlaps satisfy certain “essentially finite 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. Earlier results for fractal measures with overlaps rely on Strichartz second-order identities, which are not satisfied by the measures we consider here. This is a joint work with Wei Tang and Yuanyuan Xie.

Sponsorship/Conference/Institution

Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE)

Location

Kennesaw, GA

This document is currently not available here.

Share

COinS