论文标题
在超副企业上，光谱定理和索具的希尔伯特空间
On ultraproducts, the spectral theorem and rigged Hilbert spaces
论文作者
论文摘要
我们首先展示如何在有限的维空间中近似操作员近似统一和有限的自我接合操作员。使用超副作用，我们为近似值提供了精确的含义。在此过程中，我们了解如何获得光谱度量作为计数量度的超元素，这些测量是由有限维近似值自然产生的。然后，我们看到了如何在超副不动物中解释广义分布。最后，我们研究如何通过在有限的维近似值中计算运算符$ k $的内核，以及如何在超副措施中解释狄拉克（Dirac Deltas），以使核作为传播者$ \ langle x__ {1} | k | k | x_ {0} \ rangle $。
We start by showing how to approximate unitary and bounded self-adjoint operators by operators in finite dimensional spaces. Using ultraproducts we give a precise meaning for the approximation. In this process we see how the spectral measure is obtained as an ultralimit of counting measures that arise naturally from the finite dimensional approximations. Then we see how generalized distributions can be interpreted in the ultraproduct. Finally we study how one can calculate kernels of operators $K$ by calculating them in the finite dimensional approximations and how one needs to interpret Dirac deltas in the ultraproduct in order to get the kernels as propagators $\langle x_{1}|K|x_{0}\rangle$.
