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Zbl 1190.28005
Zhou, Denglin
Criteria for spectral gaps of Laplacians on fractals. (English)
[J] J. Fourier Anal. Appl. 16, No. 1, 76-96 (2010). ISSN 1069-5869; ISSN 1531-5851/e

Author's abstract: Surprisingly, Fourier series on certain fractals can have better convergence properties than classical Fourier series. This is a result of the existence of gaps in the spectrum of the Laplacian. In this work we prove general criteria for the existence of gaps when the Laplacian admits spectral decimation. The known examples, including the Sierpinski gasket and the level-3 Sierpinski gasket, and the new examples including the fractal-3 tree, the Hexagasket and the infinite family of tree-like fractals satisfy the criteria.
[Su Weiyi (Nanjing)]

MSC 2000:: *28A80 Fractals
42C99 Non-trigometric Fourier analysis
31C25 Dirichlet spaces

Keywords: spectral gap; Laplacian; fractal; Sierpinski gasket

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