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| One of the basic operators when studying differential equations is the Laplacian. When the underlying space is highly irregular, as happens with fractals, this operator needs to be redefined. In this talk we introduce a class of fractal spaces called fractal quantum graphs, which may not be self-similar, and obtain a Laplacian by means of Dirichlet forms.We will strongly use the theory of resistance forms developed by Kigami et al. Spectral asympotics for the eigenvalue counting function of this Laplacian in a particular type of such spaces are presented. We will also discuss some consequences of this result. |
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