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)

Revised on August 1, 2011 10:30:46
by Urs Schreiber
(82.113.99.43)