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Is this true?

Any compactly supported distribution $T\in \cal D'$ can be represented as finite sum of partial derivatives of functions.

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    A full treatment of this subject is Chpater 24 in the book "Topological Vector Spaces, Distributions and Kernels" by F. Treves, available online in major parts. @Yimin: Be careful with your first comment, you will need a constant there, a distribution may not have seminorm less or equal 1.2012-05-04

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