Distributions pp 137-152 | Cite as

Fundamental Solutions

  • J. J. Duistermaat
  • J. A. C. Kolk
Part of the Cornerstones book series (COR)


Let \(P = P(\partial ) = \sum\nolimits_{|a| \le m} {C_\alpha \partial ^\alpha }\) be a linear partial differential operator in R n with constant coefficients, as introduced in (7.5). A fundamental solution of P is a distribution \(E\ \in\ \mathcal {D}^\prime({\rm \mathbf R}^n )\ {\rm such\ that}\ P\,E - \delta,\) the Dirac measure at the origin.


Harmonic Function Open Subset Fundamental Solution Wave Operator Linear Partial Differential Operator 
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Authors and Affiliations

  1. 1.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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