Definition:Fundamental Solution
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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