Spectrum and Heat Kernel Asymptotics on General Laakso Spaces

Abstract

We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, we found the leading term of the trace of the heat kernel of a Laakso space and its spectral dimension.

v2: revised prose and cleaned up proofs v1: 23 page, 6 figures