标题： 向量值赋值在凸函数上的Klain-Schneider定理 显示英文标题

标题： A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions

摘要： 建立了一个向量值在凸函数上的Klain-Schneider定理的功能类比，提供了连续的、平移协变的、简单的值的分类。 在额外的旋转等变假设下，特征化了矩量向量的分析对应物以及一个新的上平移不变值。 前者作为一类功能内在矩中的最高阶算子出现，这些功能内在矩通过平移与功能内在体积相关联。 后者代表了一类Minkowski向量中的最高阶算子，这些Minkowski向量是在本文中引入的，并且它们在凸体上缺乏经典对应物，因为它们由于Minkowski关系而消失。 对于极端度的齐次值，获得了额外的分类结果。 显示英文摘要

摘要： A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant, simple valuations. Under additional rotation equivariance assumptions, an analytic counterpart of the moment vector is characterized alongside a new epi-translation invariant valuation. The former arises as the top-degree operator in a family of functional intrinsic moments, which are linked to functional intrinsic volumes through translations. The latter represents the top-degree operator in a class of Minkowski vectors, which are introduced in this article and which lack classical counterparts on convex bodies, as they vanish due to the Minkowski relations. Additional classification results are obtained for homogeneous valuations of extremal degrees.