Symplectic modules over Colombeau-generalized numbers
| Autor: | Konjik, Sanja, Hoermann, Guenther, Kunzinger, Michael |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Comm. Algebra 42: 3358-3577, 2014 |
| Druh dokumentu: | Working Paper |
| Popis: | We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular, we construct symplectic bases for any symplectic form on a free $\Rt$-module of finite rank. Further, we consider the general problem of eigenvalues for matrices over $\Kt$ ($\K=\R$ or $\C$) and derive normal forms for Hermitian and skew-symmetric matrices. Our investigations are motivated by applications in non-smooth symplectic geometry and the theory of Fourier integral operators with non-smooth symbols. Comment: Some typos corrected, proof of Th. 3.3 corrected |
| Databáze: | arXiv |
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