Harmonic Analysis of Translation Invariant Valuations

Semyon Alesker, Andreas Bernig, Franz E. Schuster

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)751-773
Number of pages23
JournalGeometric and Functional Analysis
Volume21
Issue number4
DOIs
StatePublished - Aug 2011

Keywords

  • Valuation
  • algebraic integral geometry
  • isoperimetric inequality
  • tensor valuation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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