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Distributions pp 271-285 | Cite as

Fundamental Solutions and Fourier Transform

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

Abstract

The Fourier transform in s is a very useful tool in the analysis of linear partial differential operators \(P(D) = \sum\limits_{|\alpha | \le m} {c_\alpha D^\alpha }\ \rm {in}\ \rm \mathbf {R}^n\) with constant coefficients s then (14.10) implies \(\mathcal {F}\,(P(D)u) = P(\xi )\,\mathcal{F}\,u.\)

Keywords

Fundamental Solution Polynomial Function Elliptic Operator Polynomial Growth Principal Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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