Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2011 | Book

Introduction Read chapter Read first chapter

Fourier Integral Operators

Author: J.J. Duistermaat

Publisher: Birkhäuser Boston

Book Series : Modern Birkhäuser Classics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

More than twenty years ago I gave a course on Fourier Integral Op­ erators at the Catholic University of Nijmegen (1970-71) from which a set of lecture notes were written up; the Courant Institute of Mathematical Sciences in New York distributed these notes for many years, but they be­ came increasingly difficult to obtain. The current text is essentially a nicely TeXed version of those notes with some minor additions (e.g., figures) and corrections. Apparently an attractive aspect of our approach to Fourier Integral Operators was its introduction to symplectic differential geometry, the basic facts of which are needed for making the step from the local definitions to the global calculus. A first example of the latter is the definition of the wave front set of a distribution in terms of testing with oscillatory functions. This is obviously coordinate-invariant and automatically realizes the wave front set as a subset of the cotangent bundle, the symplectic manifold in which the global calculus takes place.

Table of Contents

Frontmatter
Chapter 0. Introduction
Abstract
DoNotReleaseTextContentMissing
J. J. Duistermaat
Chapter 1. Preliminaries
Abstract
We assume the basic concepts of distribution theroy (as for instance in Hörmander [44], Ch. 1), Manufolds and vector bundles to be known.
J. J. Duistermaat
Chapter 2. Local Theory of Fourier Integrals
Abstract
In this section we generalize the classes of amplitude function encountered in the Introduction and in Section 1.2, and we collect some useful properties of these “symbols spaces.”
J. J. Duistermaat
Chapter 3. Symplectic Differential Geometry
Abstract
We start this chapter with a brief review of the differential geometry we will need.
J. J. Duistermaat
Chapter 4. Global Theory of Fourier Integral Operators
Abstract
In this section we give a more detailed description of the line bundle L that was indicated at the end of Section 2.3.
J. J. Duistermaat
Chapter 5. Applications
Abstract
Let X be an n-dimensional paracompact operator C ∞ manifold, P L(X) a property supported pseudodiffential oprator of order m On X with homogeneous prinicipal symbol of degrees m.
J. J. Duistermaat
Backmatter
Metadata
Title
Fourier Integral Operators
Author
J.J. Duistermaat
Copyright Year
2011
Publisher
Birkhäuser Boston
Electronic ISBN
978-0-8176-8108-1
Print ISBN
978-0-8176-8107-4
DOI
https://doi.org/10.1007/978-0-8176-8108-1

Premium Partner

    Image Credits