Spectrum and Heat Kernel Asymptotics on General Laakso Spaces

2009/12/11 by Matthew Begue, Begue, Matthew, Levi DeValve +5
Mathematics · #34B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:34B20

paper · pdf · doi:10.48550/arxiv.0912.2176

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

arxiv created 2010/02/25 · arxiv updated 2010/02/26

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.

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