标题： 关于一类Fréchet函数空间R^n上的稠密子空间 显示英文标题

标题： On dense subspaces in a class of Fréchet function spaces on R^n

摘要： 在处理 R^n 上函数空间中的具体问题时，有时会很有帮助的是拥有由某种特定类型的函数组成的稠密子空间，且这些函数针对所考虑的问题进行了调整。 我们给出一个定理，该定理允许人们在常见的 Fréchet 函数空间中写下许多这样的子空间。 这些子空间的形式均为 $\{pf_0 | p\in{\cal P}\}$，其中 $f_0$是固定函数，而 ${\cal P}$是一个函数代数。 经典结果如多项式的 Stone-Weierstrass 定理和 Hermite 函数的完备性通过这个定理相互关联。 显示英文摘要

摘要： When dealing with concrete problems in a function space on R^n, it is sometimes helpful to have a dense subspace consisting of functions of a particular type, adapted to the problem under consideration. We give a theorem that allows one to write down many of such subspaces in commonly occurring Fr\'echet function spaces. These subspaces are all of the form $\{pf_0 | p\in{\cal P}\}$ where $f_0$ is a fixed function and ${\cal P}$ is an algebra of functions. Classical results like the Stone-Weierstrass theorem for polynomials and the completeness of the Hermite functions are related by this theorem.