Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions.
As a research programme, it was started by the Japanese mathematician Mikio Sato in 1959.
It derives its meaning from the fact that the differential operator is right-invertible in several function spaces.
It helps in the simplification of the proofs due to an algebraic description of the problem considered.
The sheaf of microlocal functions on M is given as[2] where A microfunction can be used to define a Sato's hyperfunction.