What is "hyperfunction"

n. 1 (context mathematics English) A generalization of a function 2 (context medicine English) Abnormally elevated function

In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato in 1958, building upon earlier work by Grothendieck and others. In Japan, they are usually called the Sato's hyperfunctions.