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Spectral analysis of
Laplacians on the Vicsek set
Denglin Zhou |
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Vol. 241 (2009), No. 2, 369–398
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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. |
Keywords
analysis on fractals, spectral analysis, Vicsek set,
Laplace operator
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Mathematical Subject Classification 2000
Primary: 28A80, 42C99
Secondary: 31C25
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Milestones
Received: 31 May 2008
Revised: 5 October 2008
Accepted: 8 December 2008
Published: 1 June 2009
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Authors |
| Denglin Zhou | |
| University of Waterloo Department of Pure Mathematics 200 University Avenue West Waterloo, ON N2L3G1 Canada |
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