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 $\{pf_0  p\in{\cal P}\}$ where $f_0$ is a fixed function and ${\cal P}$ is an algebra of functions. Classical results like the StoneWeierstrass theorem for polynomials and the completeness of the Hermite functions are related by this theorem.
 Publication:

arXiv eprints
 Pub Date:
 December 1994
 arXiv:
 arXiv:functan/9412003
 Bibcode:
 1994funct.an.12003D
 Keywords:

 Mathematics  Functional Analysis
 EPrint:
 14 pages, no figures, plain Tex