Characterizations of all continuous, additive and GL(n)-equivariant endomorphisms of the space of convex functions on a Euclidean space Rn, of the subspace of convex functions that are finite in a neighborhood of the origin, and of finite convex functions are established. Moreover, all continuous, additive, monotone endomorphisms of the same spaces, which are equivariant with respect to rotations and dilations, are characterized. Finally, all continuous, additive endomorphisms of the space of finite convex functions of one variable are characterized.
en
Project title:
Affine isoperimetrische Ungleichungen: P31448-N35 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
