Fundamental solution of a linear differential operator

A fundamental solution of a linear differential operator

P (D)

is a distribution

E

satisfying

P (D) E = δ_{0}

.

Table of contents
- Malgrange–Ehrenpreis theorem Fundamental solution of a linear differential operator
- Retarded fundamental solution Fundamental solution of a linear differential operator

Malgrange–Ehrenpreis theorem

Every nonzero constant-coefficient linear partial differential operator has a distributional fundamental solution.

Retarded fundamental solution

A retarded fundamental solution is supported in a chosen forward region, such as

[0, \infty)

for an ordinary differential operator.

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