27 citations · 34 across the 18 of their papers we have counts for
21 papers
Hadwiger's Theorem on hyperbolic space
Jonas Knoerr
We present a proof classifying continuous isometry invariant valuations on polytopes in hyperbolic space as linear combinations of the intrinsic volumes. The argumen…
Isometry invariant valuations on spherical polytopes
Jonas Knoerr
We show that every continuous and isometry invariant valuation on spherical polytopes is a linear combination of the spherical intrinsic volumes. The proof relies on a weak differe…
Rigid motion invariant valuations on polytopes
Jonas Knoerr
We show that any measurable, translation and -invariant valuation on polytopes in is a linear combination of the intrinsic volumes, which extends Had…
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…
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…
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.…
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…
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…
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…
From valuations on convex bodies to convex functions
Jonas Knoerr, Jacopo Ulivelli
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a…
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…
Equivariant Endomorphisms of Convex Functions
Georg C. Hofstätter, Jonas Knoerr
Characterizations of all continuous, additive and -equivariant endomorphisms of the space of convex functions on a Euclidean space , of the subspace o…
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…
Smooth valuations on convex functions
Jonas Knoerr
We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We descr…
The support of dually epi-translation invariant valuations on convex functions
Jonas Knoerr
We study dually epi-translation invariant valuations on cones of convex functions containing the space of finite-valued convex functions. The existence of a homogeneous decompositi…