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I am trying to get familiar with hyperfunctions, and I do have some familiarity with the classical theory of distributions.

I am wondering whether hyperfunctions have any advantages over distributions. Are there any applications of the former which cannot be obtained using the latter? Any important examples?

I was told one general property of hyperfunctions which seems to be important and which is not satisfies by usual distributions: the sheaf of hyperfunctions (on a real analytic manifold) is injective.

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    $\begingroup$ I recommend to read Hormander, Analysis of Partial Differential Operators, vol. I, Ch. 9, where this is explained. $\endgroup$
    – Alexandre Eremenko
    Commented Aug 23, 2015 at 20:26

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