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Pure point spectrum for the Laplacian on unbounded nested fractals. (English) Zbl 0965.35103
The author considers the Laplace operator on unbounded nested fractals which consist of self-similar and finitely ramified sets (invariant for a large group of symmetries) and shows that the set of Neumann-Dirichlet eigenvalues leads to pure-point spectrum with compactly supported eigenfunctions. The main results are given in three theorems which are proven by using only symmetry properties.

35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
28A80 Fractals
Full Text: DOI
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