6 papers
Zonal valuations on convex bodies
Jonas Knoerr
A complete classification of all zonal, continuous, and translation invariant valuations on convex bodies is established. The valuations obtained are expressed as principal value i…
Polynomial valuations on convex functions and their maximal extensions
Jonas Knoerr, Jacopo Ulivelli
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extensi…
A geometric decomposition for unitarily invariant valuations on convex functions
Jonas Knoerr
Valuations on the space of finite-valued convex functions on that are continuous, dually epi-translation invariant, as well as -invariant are complete…
Equivariant Valuations on Convex Functions
Georg C. Hofstätter, Jonas Knoerr
We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant…
The homogeneous decomposition of dually translation invariant valuations on Lipschitz functions on the sphere
Andrea Colesanti, Jonas Knoerr, Daniele Pagnini
We show that every continuous and dually translation invariant valuation on the space of Lipschitz functions on the unit sphere of , , can be decomposed unique…
Monge-Ampère operators and valuations
Jonas Knoerr
Two classes of measure-valued valuations on convex functions related to Monge-Ampère operators are investigated and classified. It is shown that the space of all valuations with va…