Two minicourses on analytic microlocal analysis

TL;DR

This paper provides an accessible introduction to analytic microlocal analysis, focusing on metaplectic FBI transforms and techniques in weighted spaces of holomorphic functions, based on minicourses from a 2013 workshop.

Contribution

It offers a clear exposition of global metaplectic FBI transforms and analytic microlocal analysis techniques in exponential weighted spaces, filling a gap in accessible educational resources.

Findings

Introduction to metaplectic FBI transforms

Development of analytic microlocal analysis techniques

Applications in exponential weighted spaces

Abstract

These notes correspond roughly to the two minicourses prepared by the authors for the workshop on Analytic Microlocal Analysis, held at Northwestern University in May 2013. The first part of the text gives an elementary introduction to some global aspects of the theory of metaplectic FBI transforms, while the second part develops the general techniques of the analytic microlocal analysis in exponentially weighted spaces of holomorphic functions.