Resumen de Spectral analysis of Laplacians on the Vicsek set

Denglin Zhou

• We find the spectral decimation function for the standard Laplacian on the symmetric Vicsek set, expressed in terms of Chebyshev polynomials. This allows us to determine the order of the eigenvalues of the Laplacian, describe their asymptotic behavior and prove that there exist gaps in the spectrum.