解析泛函的载体锥
Carrier cones of analytic functionals
摘要：
证明了由其Fourier变换属于Schwartz空间$\mathcal D$的整解析函数组成的空间$S^0(R^d)$上的每一个连续线性泛函在$R^d$中有唯一的极小载体锥，该载体锥代替支撑.证明是基于一个相关的分解定理的元素的空间$S^0(K)$自然与封闭锥$K\subset R^d$。这些结果对于非定域量子场论的应用是必不可少的，它们类似于以前对于Gelfand-Shilov空间$S^0_α$上的泛函所得到的结果，但是它们的推导更加复杂，因为$S^0(K)$不是DFS空间，并且具有更复杂的拓扑结构。
英文摘要：
We prove that every continuous linear functional on the space $S^0(R^d)$ consisting of the entire analytic functions whose Fourier transforms belong to the Schwartz space $\mathcal D$ has a unique minimal carrier cone in $R^d$, which substitutes for the support. The proof is based on a relevant decomposition theorem for elements of the spaces $S^0(K)$ associated naturally with closed cones $K\subset R^d$. These results, essential for applications to nonlocal quantum field theory, are similar to those obtained previously for functionals on the Gelfand-Shilov spaces $S^0_α$, but their derivation is more sophisticated because $S^0(K)$ are not DFS spaces and have more complicated topological structure.
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