Definition:Dipole
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Definition
Let $\phi \in \map \DD \R$ be a test function.
Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution.
Then for any $\phi$ the distributional derivative of $\delta$ is known as the dipole and is given by:
- $\ds \map {\delta'} \phi = - \map {\phi'} 0$
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 6.2$: A glimpse of distribution theory. Derivatives in the distributional sense