Distributions pp 271-285 | Cite as

Fundamental Solutions and Fourier Transform

Part of the Cornerstones book series (COR)


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 \(\mathcal {F}\,(P(D)u) = P(\xi )\,\mathcal{F}\,u.\)


Fundamental Solution Polynomial Function Elliptic Operator Polynomial Growth Principal Symbol 
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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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