Valuation theory of indefinite orthogonal groups
| Autor: | Bernig, Andreas, Faifman, Dmitry |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Journal of Functional Analysis 273 (2017), 2167-2247 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jfa.2017.06.005 |
| Popis: | Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant valuations, generalizing Hadwiger's classification of Euclidean isometry-invariant valuations. As a result of independent interest, we identify within the space of translation-invariant valuations the class of Klain-Schneider continuous valuations, which strictly contains all continuous translation-invariant valuations. The operations of pull-back and push-forward by a linear map extend naturally to this class. Comment: 65 pages; Some details in proofs added and minor mistakes corrected, an appendix on wave front sets of G-invariant distributions and a section on the linear algebra of O(p,q) added. Accepted for publication in Journal of Functional Analysis |
| Databáze: | arXiv |
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