Spectrum of the Laplacian on the Vicsek Set 'with no loose ends'
| Autor: | Robert S. Strichartz, Sophia Zhu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Polynomial Decimation Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Mathematics::Spectral Theory Lipschitz continuity 01 natural sciences 010305 fluids & plasmas Renormalization Fractal Mathematics - Analysis of PDEs Modeling and Simulation 0103 physical sciences FOS: Mathematics Countable set Geometry and Topology 0101 mathematics Laplace operator Mathematics Analysis of PDEs (math.AP) |
| Popis: | We study the spectral properties of a fractal the Vicsek set “with no loose ends” (VNLE) obtained from the standard Vicsek set (VS) by making a countable number of identifications of points so that all the line segments in VS become circles in VNLE. We show that the standard Laplacian on VNLE satisfies spectral decimation with the same cubic renormalization polynomial as for VS, and thereby give a complete description of all eigenfunctions of the Laplacian. We then study the restrictions of eigenfunctions to the large circles in VNLE and prove that these are Lipschitz functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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