Good evening to all,
For
, I am considering the mapping:
,
I would like to show that
actually maps
to
.
I have done the following: First I notice that:
Hence to show the intended I must show that when the operator
is applied on a function
then the outcome is a function which is also in
.
Using rules of calculus I can argue that the function
is continous. Now I just need to show that this function has compact support and my job is done. The support of a function
is the smallest closed set outside which the function is equal to zero, i.e.
. Because I don't have a specific function to work with I'm finding it a bit difficult to show the case of compact support. How do I show that the function
has compact support?
Thanks.