| Autor: |
Band, Ram, Bersudsky, Michael, Fajman, David |
| Rok vydání: |
2015 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s11005-016-0926-7 |
| Popis: |
We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\sqrt{2}$ (also known as the A4 paper). In $\R^{n}$ the domains are boxes which generalize the mentioned planar rectangle. The symmetries of those domains reveal a special structure of their eigenfunctions, which we call folding\textbackslash{}unfolding. This structure affects the nodal set of the eigenfunctions, which in turn allows to derive necessary conditions for Courant-sharpness. In addition, the eigenvalues of these domains are arranged as a lattice which allows for a comparison between the nodal count and the spectral position. The Courant-sharpness of most eigenvalues is ruled out using those methods. In addition, this analysis allows to estimate the nodal deficiency - the difference between the spectral position and the nodal count. |
| Databáze: |
arXiv |
| Externí odkaz: |
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