I am looking for some slick or simple proof that distributions are a special case of hyperfunctions. Furthermore, what is the intuition behind this fact? Why should one think of hyperfunctions as 'distributions of infinite order' as wikipedia says?
I have not studied hyperfunctions, so I only think of them naively as the difference of two holomorphic functions (in one variable) on the real line.
[By the way, I think making a hyperfunctions tag may be worth considering.]