Category:Distributional Derivatives

From ProofWiki
Jump to navigation Jump to search

This category contains results about Distributional Derivatives.


Let $\phi \in \map \DD \R$ be a test function.

Let $T \in \map {\DD'} \R$ be a distribution.


The distributional derivative $\ds \dfrac {\d T} {\d x} \in \map {\DD'} \R$ is defined by:

$\map {\dfrac {\d T} {\d x}} \phi := - \map T {\dfrac {\d \phi} {\d x}}$