35 citations · 75 across the 8 of their papers we have counts for
8 papers
The Legendre transform, the Laplace transform and valuations
Jin Li
We first prove that the Legendre transform is the only continuous and contravariant valuation that behaves as a conjugation of two important translations on super-…
Dualities and endomorphisms of pseudo-cones
Yun Xu, Jin Li, Gangsong Leng
In this paper we study a class of convex sets which are called closed pseudo-cones and study a new duality of this class. It turns out that the duality characterizes closed pseudo-…
covariant function-valued valuations
Jin Li
Classifications of covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, ar…
SL() contravariant vector valuations
Jin Li, Dan Ma, Wei Wang
All SL() contravariant vector valuations on polytopes in are completely classified without any additional assumptions. The facet vector is defined. It turns out to…
Laplace transforms and valuations
Jin Li, Dan Ma
It is proved that the classical Laplace transform is a continuous valuation which is positively GL covariant and logarithmic translation covariant. Conversely, these propertie…
Minkowski Valuations on polytopes
Jin Li, Gangsong Leng
For , Ludwig, Haberl and Parapatits classified Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity an…
Affine function valued valuations
Jin Li
A classification of SL contravariant, continuous function valued valuations on convex bodies is established. Such valuations are natural extensions of SL contravariant $L…
Orlicz valuations
Jin Li, Gangsong Leng
In this paper, Orlicz valuations compatible with transforms are classified. Unlike their analogs, the identity operator and the reflection operator are the only $SL(n…