Technique of studying linear partial differential equations
Not to be confused with the common phrase "algebraic analysis of [a subject]", meaning "the algebraic study of [that subject]"
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. Semantically, it is the application of algebraic operations on analytic quantities. As a research programme, it was started by the Japanese mathematician Mikio Sato in 1959.[1] This can be seen as an algebraic geometrization of analysis. 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.
^Kashiwara & Kawai 2011, pp. 11–17.
and 28 Related for: Algebraic analysis information
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