6 papers
Polynomial local functionals on convex functions
Jonas Knoerr
We show that every continuous local functional on the space of finite convex functions on is a valuation. This relation is used to establish a homogeneous decomposit…
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…
Integral representation of polynomial local functionals on convex functions
Jonas Knoerr
Integral representations for continuous polynomial local functionals on convex functions are established in terms of a finite family of polynomials. This result is obtained by appr…
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…
A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions
Jonas Knoerr
Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions.…