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

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.