The existence of a homogeneous decomposition for continuous and epi-translation invariant
valuations on super-coercive functions is established. Continuous and epi-translation …

A complete classification of all continuous, epi-translation and rotation invariant valuations
on the space of super-coercive convex functions on\({\mathbb {R}}^{n}\) is established. The …

A classification of SL (n) SL (n) contravariant Minkowski valuations on convex functions and
a characterization of the projection body operator are established. The associated LYZ …

New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex
functions are obtained, and the Klain–Schneider theorem on convex functions is …

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 decomposition …

The notion of a valuation on convex bodies is very classical; valuations on a class of
functions have been introduced and studied by M. Ludwig and others. We study an explicit …

The aims of this paper are to develop the LYZ ellipsoid and Petty projection body for log-
concave functions, which correspond to the LYZ ellipsoid and Petty projection body for …

A new class of continuous valuations on the space of convex functions on ℝ n is introduced.
On smooth convex functions, they are defined for i= 0,..., n by u↦∫ ℝ n ζ (u (x), x,▽ u (x))[D 2 …

Volume, polar volume and Euler characteristic for convex functions - ScienceDirect Skip to
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Characterizations of all continuous, additive and GL (n)-equivariant endomorphisms of the
space of convex functions on a Euclidean space R n, of the subspace of convex functions …