nLab
microlocalization

Microlocalization is a tool invented by Mikio Sato to study linear partial differential equations (as a part of his algebraic analysis program) not only locally in space but also locally in momentum variable. It is a purely algebraic theory that was also continued in parallel by analysts, like Hormander, giving the domain of microlocal analysis.

Sato’s theory of microlocalization was first described in the setting of D-modules:

• M. Kashiwara, Kawai, Kimura: foundations of algebraic analysis.

It was then extended by M. Kashiwara and P. Schapira to a purely sheaf theoretical theory.

This theory of microlocalization of (ind)-sheaves was developped in the following works:

• Masaki Kashiwara, Pierre Schapira, Ind-sheaves, distributions and microlocalization, describes the program.
• Masaki Kashiwara, Pierre Schapira, Florian Ivorra?, Ingo Waschkies Microlocalization of ind-sheaves, gives the main results and proofs.
• Masaki Kashiwara, Pierre Schapira Ind-sheaves, SMF, gives a complete account of the theory.

A good overview of the theory can by found at:

• Pierre Schapira Derived categories for the analyst (2010)