Spectral analysis beyond ${\mathrm{\ell }}^2$ on Sierpinski lattices

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 ${\mathrm{\ell }}^p$ spaces. Second, we characterize all the spectral points for the lattices with a boundary point.