arxiv: 1008.3768 · v2 · pith:TXEGC4NOnew · submitted 2010-08-23 · 🧮 math.DG

Harmonic analysis of translation invariant valuations

Semyon Alesker , Andreas Bernig , Franz E. Schuster This is my paper

classification 🧮 math.DG

keywords invariantvaluationstranslationcontinuoustypeanalysisapplicationbivaluations

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The decomposition of the space of continuous and translation invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger type theorem for continuous translation invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.

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Harmonic analysis of translation invariant valuations

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