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Semi-Classical Wavefront Set and Fourier Integral Ivana Alexandrova

Summary: Semi-Classical Wavefront Set and Fourier Integral
Ivana Alexandrova
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3,
Tel.: 1-416-946-0318, Fax: 1-416-978-4107, email: alexandr@math.toronto.edu
March 1, 2005
Here we define and prove some properties of the semi-classical wavefront set. We
also define and study semi-classical 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 Introduction
In this article we define the semi-classical wavefront set and Fourier integral operators and
establish some of the properties.
Semi-classical 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
semi-classical Fourier integral operators, while for the unitary group , U(t) = e- i


Source: Alexandrova, Ivana - Department of Mathematics and Statistics, State University of New York at Albany
Alexandrova, Ivana - Department of Mathematics, East Carolina University


Collections: Mathematics