Harmonic analysis of translation invariant valuations

Details Harmonic analysis of translation invariant valuations Harmonic analysis of translation invariant valuations

2010-08-23

arxiv.org/abs/1008.3768v2

Geom. Funct. Anal. 21 (2011), 751-773

Mathematics

Differential Geometry

29 pages; title, abstract and structure revised; to appear in GAFA

Scientific paper

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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