Birkhoff normal forms for Fourier integral operators

Alexei Iantchenko Malmö University

We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical transformation was assumed to be of real hyperbolic type. In [IS] this assumption was relaxed considerably, to what we think are the natural conditions.

This is a joint work with J. Sjöstrand.

References.

[Ia] A. Iantchenko, La forme normale de Birkhoff pour un opérateur intégral de Fourier, Asymptotic Analysis, 17(1)(1998), 71–92.

[IS] A. Iantchenko and J. Sjöstrand, Birkhoff normal forms for Fourier integral operators II, preprint, 2001.

http://xxx.lanl.gov/abs/math.SP/0111134