Spectrum and Heat Kernel Asymptotics on General Laakso Spaces
Matthew Begue, Levi DeValve, David Miller, Benjamin Steinhurst
TL;DR
This paper develops a method to construct general Laakso spaces and analyzes the spectral properties of the Laplacian, including the heat kernel's leading term and spectral dimension, advancing understanding of fractal geometries.
Contribution
It introduces a novel construction method for general Laakso spaces and computes their Laplacian spectrum and heat kernel asymptotics.
Findings
Calculated the spectrum and multiplicities of the Laplacian on Laakso spaces
Determined the leading term of the heat kernel trace
Identified the spectral dimension of 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.
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