Definition:Fundamental Solution

Definition

Let $\delta$ be the Dirac delta distribution.

Let $D$ be a differential operator with constant coefficients.

A fundamental solution is a distribution $E \in \map {\DD'} {\R^d}$ such that:

$DE = \delta$

Also see

• Results about fundamental solutions can be found here.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous): Chapter $\S 6.5$: Fourier transform of (tempered) distributions