Distributions
Submitted by Structure on Sun, 12/16/2007 - 16:53.
Distributions are continuous linear applications on different test functions.
Usually test functions are in the space with topology
defined by convergent sequence, as follows
A sequence is convergent to
if and only if there is a compact
such as for all
and for all
,
![]() |
We write for the space
There is a useful equivalent condition for a linear map on to be a distribution:
Theorem. A linear map u on is a distribution if and only if
, there are constants
such as
we have
![]() |
The minimal integer k in this definition is called the order of distribution on K.
An important example of distribution is Dirac defined by
![]() |
Dirac is a distribution of order zero.