## Pseudodifferential operators, corners and singular limits.(English)Zbl 0743.58033

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 217-234 (1991).
[For the entire collection see Zbl 0741.00019.]
In this expository talk the author describes the problems appearing in the construction of a pseudodifferential calculus adapted to corners.
In particular he describes the properties one should expect of such a calculus which corresponds to the microlocalization of a Lie algebra of vector fields. This gives necessary conditions on the Lie algebra. The author describes also how the symbolic calculus can be applied in the solution of analytic questions related to the Lie algebra, especially to the inversion of elliptic elements of the enveloping algebra.
At the end the author describes many applications: $$K$$-theory, Bergman geometry, adiabatic limit of a fibration, analytic surgery...
Reviewer: B.Helffer (Paris)

### MSC:

 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J15 Relations of PDEs on manifolds with hyperfunctions

Zbl 0741.00019