标题： 一个关于凸函数上光滑估值的Paley-Wiener-Schwartz定理 显示英文标题

标题： A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions

摘要： 连续对偶上图不变的凸函数值在 Goodey-Weil 分布的傅里叶-拉普拉斯变换下被刻画。 这一描述被用来获得这些值在估值空间上的平移群自然表示的光滑向量的积分表示。 作为应用，建立了所有闭合和仿射不变子空间的完整分类，从而得到了由混合 Monge-Ampère 算子定义的估值的密度结果。 显示英文摘要

摘要： Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations of the smooth vectors of the natural representation of the group of translations on the space of these valuations. As an application, a complete classification of all closed and affine invariant subspaces is established, yielding density results for valuations defined in terms of mixed Monge-Amp\`ere operators.