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Distribution Theory/Distributions

Preliminaries, convergence, TVSEdit

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 propertiesEdit

Distributions and functionsEdit

Operations on distributionsEdit

When given a distribution, we can do several things with it. These include: