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arXiv · 1910.01771

Spectral analysis beyond $\ell^2$ on Sierpinski lattices

Shiping Cao·Yiqi Huang·Hua Qiu·Robert S. Strichartz·Xiaohan Zhu
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Abstract

We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of $\mathbb{C}$, remains the same for any $\ell^p$ spaces. Second, we characterize all the spectral points for the lattices with a boundary point.

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Shiping Cao, Yiqi Huang, Hua Qiu, Robert S. Strichartz, Xiaohan Zhu. 2019-10-04. Spectral analysis beyond $\ell^2$ on Sierpinski lattices. https://arxiv.org/abs/1910.01771

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