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Abstract
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We find the spectral decimation
function for the standard Laplacian on the symmetric Vicsek set, expressed in terms
of Chebyshev polynomials. This allows us to determine the order of the eigenvalues of
the Laplacian, describe their asymptotic behavior and prove that there exist gaps in
the spectrum.
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Keywords
analysis on fractals, spectral analysis,
Vicsek set, Laplace operator
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Mathematical Subject Classification
Primary: 28A80, 42C99
Secondary: 31C25
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Milestones
Received: 31 May 2008
Revised: 5 October 2008
Accepted: 8 December 2008
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