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  "body": "\n## Summary\n\nA hyperfunction on an open set of the real line is a formal difference of boundary values of holomorphic functions.\nOne function lives above the real axis and the other below it.\nHyperfunctions were introduced by Mikio Sato and generalize distributions.\nThey form a flabby sheaf, so local hyperfunctions can always be glued and extended.\nThey are the basic objects of algebraic analysis of linear partial differential equations.\n\n## Explanations\n\n### L1 human\n\nTake a holomorphic function $F$ above the real axis and another one below it.\nTheir \"jump\" across the real axis, $F(x + i0) - G(x - i0)$, is a hyperfunction, even when neither limit exists as a function.\nAdding the same holomorphic function on both sides does not change the jump, so such pairs count as the same hyperfunction.\nFor example, the jump of $-1/(2\\pi i z)$ across the real axis is the Dirac delta.\n",
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