Abstract
Let 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 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.
Original language | English |
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Pages (from-to) | 2167-2247 |
Number of pages | 81 |
Journal | Journal of Functional Analysis |
Volume | 273 |
Issue number | 6 |
DOIs | |
State | Published - 15 Sep 2017 |
Externally published | Yes |
Keywords
- Convex geometry
- Hadwiger's theorem
- Intrinsic volumes
- Valuation theory