论文标题
凸功能的模棱两可的内态性
Equivariant Endomorphisms of Convex Functions
论文作者
论文摘要
所有连续，加性和$ \ MATHRM {gl}（n）$ - 凸空间的均等内态性的表征在Euclidean Space $ \ Mathbb {r}^n $上起作用，在convex函数的子空间中，该函数的核心函数是有限的。此外，表征了相同空间的所有连续，添加剂，单调的内态，相对于旋转和扩张而言是均等的。最后，表征了一个变量的有限凸功能空间的所有连续，加性内态。
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the origin, and of finite convex functions are established. Moreover, all continuous, additive, monotone endomorphisms of the same spaces, which are equivariant with respect to rotations and dilations, are characterized. Finally, all continuous, additive endomorphisms of the space of finite convex functions of one variable are characterized.
