Spectral structure of the Neumann–Poincaré operator on tori
| Autor: | Kazunori Ando, Yong-Gwan Ji, Yoshihisa Miyanishi, Hyeonbae Kang, Daisuke Kawagoe |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Hilbert space Boundary (topology) Compact operator 01 natural sciences Neumann–Poincaré operator Mathematics - Spectral Theory Mathematics - Functional Analysis 010101 applied mathematics symbols.namesake Operator (computer programming) 47A45 31B25 Bounded function symbols Mathematics::Metric Geometry 0101 mathematics Numerical range Mathematical Physics Analysis Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 36:1817-1828 |
| ISSN: | 1873-1430 0294-1449 |
| DOI: | 10.1016/j.anihpc.2019.05.002 |
| Popis: | We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincar\'e operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a property. It is done by decomposing the Neumann--Poincar\'e operator on tori into infinitely many self-adjoint compact operators on a Hilbert space defined on the circle using the toroidal coordinate system and the Fourier basis, and then by proving that the numerical range of infinitely many operators in the decomposition has both positive and negative values. Comment: 14 pages |
| Databáze: | OpenAIRE |
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