Distributions with Compact Support

Part of the Cornerstones book series (COR)


If u is locally integrable on an open set X in R n and has compact support, the integral \(u(\phi ) = \int_X {u(x)\phi (x)\ dx}\) is absolutely convergent for every \(\phi \in C^\infty (X),\) as follows from a slight adaptation of the proof of Theorem 3.5. More generally, every distribution with compact support can be extended to a continuous linear form on \(C^\infty (X).\)


Compact Subset Linear Space Linear Form Compact Support Open Neighborhood 
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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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