5 papers · 1 filter
Translation invariant area measures on convex bodies
Jonas Knoerr
We introduce the space of continuous and translation invariant area measures, which are measure-valued functionals on the space of convex bodies satisfying a certain locality condi…
Unitarily invariant valuations on convex functions
Jonas Knoerr
Continuous, dually epi-translation invariant valuations on the space of finite-valued convex functions on that are invariant under the unitary group are investigated…
Localization of valuations and Alesker's irreducibility theorem
Georg C. Hofstätter, Jonas Knoerr
We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independentl…
Smooth valuations on convex bodies and finite linear combinations of mixed volumes
Jonas Knoerr
It is shown that Alesker's solution of McMullen's conjecture implies the following stronger version of the conjecture: Every continuous, translation invariant, -homogeneous valu…
Singular valuations and the Hadwiger theorem on convex functions
Jonas Knoerr
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions…