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Criteria for spectral gaps of Laplacians on fractals. (English) Zbl 1190.28005
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.
MSC:
28A80Fractals
42C99Non-trigonometric Fourier analysis
31C25Dirichlet spaces
References:
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