5 papers · 1 filter
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…
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…
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.…
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…