Criteria for Spectral Gaps of Laplacians on Fractals
Criteria for Spectral Gaps of Laplacians on Fractals
复制标题
分形上拉普拉斯算子的谱间隙准则
DOI：
10.1007/s00041-009-9087-8
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发表时间：
2010
影响因子：
1.2
通讯作者：
D. Zhou
中科院分区：
文献类型：
--
作者：
D. Zhou
令人惊讶的是，某些分形上的傅里叶级数可以比经典傅里叶级数具有更好的收敛特性。这是拉普拉斯算子的频谱中存在间隙的结果。在这项工作中，我们证明了存在的差距时，拉普拉斯算子承认频谱抽取的一般标准。已知的例子，包括Sierpinski垫片和3级Sierpinski垫片，和新的例子，包括分形3树，Hessenbasket和无限族的树状分形满足该标准。
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.