convex function; valuation on functions; simple valuation
en
Abstract:
We study continuous, dually epi-translation invariant valuations on ℂⁿ that are invariant under the unitary group and we give a description of all valuations belonging to the dense subspace of smooth valuations. In addition, we give a classification of all simple valuations and we introduce a version of the Klain function for valuations of this type. These results are then used to show that a unitarily invariant valuation is uniquely determined by its restriction to a certain finite family of subspaces of ℂⁿ.
