Valuation theory of indefinite orthogonal groups

Andreas Bernig, Dmitry Faifman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)2167-2247
Number of pages81
JournalJournal of Functional Analysis
Volume273
Issue number6
DOIs
StatePublished - 15 Sep 2017
Externally publishedYes

Funding

FundersFunder number
D.F.
Judith Rothschild Foundation
California Department of Fish and GameBE 2484/5-1, BE 2484/5-2
Natural Sciences and Engineering Research Council of Canada

    Keywords

    • Convex geometry
    • Hadwiger's theorem
    • Intrinsic volumes
    • Valuation theory

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