Spectrum and Heat Kernel Asymptotics on General Laakso Spaces
Classical Analysis and ODEs
2010-02-25 v2 Functional Analysis
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.
Cite
@article{arxiv.0912.2176,
title = {Spectrum and Heat Kernel Asymptotics on General Laakso Spaces},
author = {Matthew Begue and Levi DeValve and David Miller and Benjamin Steinhurst},
journal= {arXiv preprint arXiv:0912.2176},
year = {2010}
}
Comments
v2: revised prose and cleaned up proofs v1: 23 page, 6 figures