## Abstract

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 "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. 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.

Original language | American English |
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State | Published - Jun 13 2017 |

Event | Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals - Duration: Jun 13 2017 → … |

### Conference

Conference | Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals |
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Period | 06/13/17 → … |

## Keywords

- Factal Laplacians
- One-dimensional
- Spectral dimension

## DC Disciplines

- Mathematics
- Physical Sciences and Mathematics