Zoom, Online seminar
(線上演講 Zoom)
Some Facts in Fractal Spectral Measure Theory
Zhi-Yi Wu (University of Oulu)
Abstract
Fractal spectral measure theory is a field connecting fractal geometry and Fourier analysis. More specifically, it is about the existence and structure of the exponential orthonormal bases on fractal measures. In this talk, I will introduce some facts about it. Specifically, I will give the proofs of the next three facts about the standard fourth-middle Cantor measure
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmu_4%24&chf=bg,s,333333&chco=ffffff)
:
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmu_4%24&chf=bg,s,333333&chco=ffffff)
is a spectral measure with a spectrum
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5CLambda_4%24&chf=bg,s,333333&chco=ffffff)
(Jorgensen and Pederson, 1998);
![](https://chart.googleapis.com/chart?cht=tx&chl=%245%5CLambda_4%24&chf=bg,s,333333&chco=ffffff)
is also a spectrum of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmu_4%24%20&chf=bg,s,333333&chco=ffffff)
(Laba and Wang first noticed this fact); there exists a spectrum
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5CLambda%24%20&chf=bg,s,333333&chco=ffffff)
of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmu_4%24&chf=bg,s,333333&chco=ffffff)
such that its Beurling dimension is zero (Dai, He and Lai, 2013).
If time permits, I will introduce the ideas of proofs about the convergence results of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmu_4%24%20&chf=bg,s,333333&chco=ffffff)
obtained by Strichartz (2006) and Dutkay et al. (2014).
Meeting Link
https://us02web.zoom.us/j/82058526043?pwd=Z0QzVXZVNDRTRkhJMG4rQ0dlSlkzUT09