411 REFERENCE · Wikibooks
Distribution Theory/Distributions
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Preliminaries, convergence, TVS
Definition:
A distribution is a linear and continuous map from to for an open .
Construction:
We now construct the LCTVS of distributions on , denoted by . Indeed, to induce the locally convex topology, we use a family of seminorms given by
for ,
where ranges over the natural numbers and over all compact subsets of .
Stability properties
Distributions and functions
Operations on distributions
When given a distribution, we can do several things with it. These include: