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math.FA2025
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…
math.MG2025★ 1 cited
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…
math.FA2025
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.…