is a distribution of zeroth order
To check that is a distribution of zeroth order (http://planetmath.org/Distribution4), we shall use condition (3) on this page (http://planetmath.org/Distribution4). First, it is clear that is a linear mapping. To see that is continuous, suppose is a compact set in and , i.e., is a smooth function with support in . We then have
Since is locally integrable, it follows that is finite, so
Thus is a distribution of zeroth order (, pp. 381).
- 1 S. Lang, Analysis II, Addison-Wesley Publishing Company Inc., 1969.
|Title||is a distribution of zeroth order|
|Date of creation||2013-03-22 13:44:28|
|Last modified on||2013-03-22 13:44:28|
|Last modified by||Koro (127)|