 
Summary: SemiClassical Wavefront Set and Fourier Integral
Operators
Ivana Alexandrova
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3,
Tel.: 14169460318, Fax: 14169784107, email: alexandr@math.toronto.edu
March 1, 2005
Abstract
Here we define and prove some properties of the semiclassical wavefront set. We
also define and study semiclassical Fourier integral operators and prove a generaliza
tion of Egorov's Theorem to manifolds of different dimensions.
Keywords and phrases: Wavefront set, Fourier integral operators, Egorov Theorem, Semi
classical analysis.
1
1 Introduction
In this article we define the semiclassical wavefront set and Fourier integral operators and
establish some of the properties.
Semiclassical Fourier integral operators have been studied in [10] where they are defined
through oscillatory integrals. Robert proves a composition formula for a general class of
semiclassical Fourier integral operators, while for the unitary group , U(t) = e i
h
