Book Review: Hyperfunctions on hypo-analytic manifolds
Pierre Schapira · Bulletin of the American Mathematical Society · 1996
Hyperfunctions were introduced by Mikio Sato [8] in the late fifties as cohomological objects built from holomorphic functions.More precisely, if M denotes an n-dimensional real analytic manifold and X a complexification of M , the sheaf B M of hyperfunctions is defined as:where O X is the sheaf of holomorphic functions on X and or M the orientation sheaf on M .Using Čech cohomology, it is then possible to represent hyperfunctions as "boundary values" of holomorphic functions defined on tuboids having M as an edge.For example, if M is an open interval of the real line R and X is an open subset of C, with X ∩ R = M, then B(M) O(X \ M)/O(X)