论文标题
对凸功能的双重跨译本不变估值的支持
The support of dually epi-translation invariant valuations on convex functions
论文作者
论文摘要
我们研究了包含有限值凸功能空间的凸函数的双向翻译不变估值。均匀分解的存在用于将分布与这种类型的每种估值相关联，类似于Goodey-weil嵌入，用于转换凸体的不变估值。估值及其相关分布之间的关系用于建立对估值的支持概念。作为一个应用程序，我们表明没有$ \ mathrm {sl}（n）$或翻译不变的估值，除了该课程中的恒定估值外，我们讨论了哪些有限价值凸功能的估值可以扩展到较大的锥体。此外，我们研究了具有紧凑支持的估值空间的一些拓扑特性。
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 is used to associate a distribution to every valuation of this type similar to the Goodey-Weil embedding for translation invariant valuations on convex bodies. The relation between the valuation and its associated distribution is used to establish a notion of support for valuations. As an application, we show that there are no $\mathrm{SL}(n)$ or translation invariant valuations except constant valuations in this class and we discuss which valuations on finite-valued convex functions can be extended to larger cones. In addition, we examine some topological properties of spaces of valuations with compact support.
