Algebraic analysis

The phrase "algebraic analysis of " is often used as a synonym for "algebraic study of", however this article is about a combination of algebraic topology, algebraic geometry and complex analysis started by Mikio Sato in 1959.

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.

See also

• Hyperfunction
• D-module
• Microlocal analysis
• Generalized function
• Edge-of-the-wedge theorem
• FBI transform
• Localization of a ring
• Vanishing cycle
• Gauss-Manin connection
• Differential algebra
• Perverse sheaf
• Mikio Sato
• Masaki Kashiwara
• Lars Hörmander

Further reading

• Masaki Kashiwara and Algebraic Analysis
• Foundations of algebraic analysis book review