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arXiv · 1602.08760

Valuation theory of indefinite orthogonal groups

Andreas Bernig·Dmitry Faifman
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Abstract

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.

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BibTeXRIS

Andreas Bernig, Dmitry Faifman. 2016-02-28. Valuation theory of indefinite orthogonal groups. https://doi.org/10.1016/j.jfa.2017.06.005

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