Spectral analysis on infinite Sierpiński gaskets
The paper is devoted to the spectral properties of the Laplacian on infinite Sierpiński gaskets. It is proved that the Laplacian with the Neumann boundary condition has pure point spectrum. Moreover, the set of eigenfunctions with compact support is complete. The same is true if the infinite Sierpiński gasket has no boundary, but is false for the Laplacian with the Dirichlet boundary condition. The spectra are found explicitly. The results are based on new formulas for eigenprojectors of the discrete Laplacians on finite Sierpiński pre-gaskets.
scientific article; zbMATH DE number 1268055
scientific article