Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

Details Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

2012-04-23

arxiv.org/abs/1204.5207v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\^ate \`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhuijsen.

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