Let and consider the Cartesian space of dimension .
(product of a distribution with a smooth function)
For a distribution, and a smooth function, their product
is the distribution given on a compactly supported smooth function by
where on the right we have the application of regarded as a continuous linear functional to the ordinary pointwise product of smooth functions .
(product of a distribution with a non-singular distributions is product of distribution with a smooth function)
The wave front set of a non-singular distribution corresponding to a smooth function , is empty (this prop.). Therefore the product of distributions (def. ) of a non-singular distribution with any distribution is defined, and given by the product of distributions with smooth functions according to def. :
See also
Created on November 7, 2017 at 16:26:25. See the history of this page for a list of all contributions to it.