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

Abstract

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 Fréchet function spaces. These subspaces are all of the form $\{p{f}_0|p\in \mathcal{P}\}$ where $f_0$ is a fixed function and $\mathcal{P}$ 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.

arXiv comment14 pages, no figures, plain Tex