Abstract
We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimation by the canonic graph approximation and the other does not. For the second fractal, we adjust to choosing a new graph approximation guided by the directed graph, which still admits spectral decimation. Then we make a full description of the Dirichlet and Neumann eigenvalues and eigenfunctions of both of these two fractals.
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Acknowledgements
Hua Qiu was supported by National Natural Science Foundation of China (Grant No. 12071213) and the Natural Science Foundation of Jiangsu Province in China (Grant No. BK20211142).
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Cao, S., Qiu, H., Tian, H. et al. Spectral decimation for a graph-directed fractal pair. Sci. China Math. 65, 2503–2520 (2022). https://doi.org/10.1007/s11425-020-1909-x
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DOI: https://doi.org/10.1007/s11425-020-1909-x