Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators

  • Nicolas Lerner

Part of the Pseudo-Differential Operators book series (PDO, volume 3)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Nicolas Lerner
    Pages 1-55
  3. Nicolas Lerner
    Pages 57-160
  4. Nicolas Lerner
    Pages 161-286
  5. Nicolas Lerner
    Pages 287-382
  6. Back Matter
    Pages 383-397

About this book

Introduction

This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H¨ ormander (Chapter 18 in the book [73]) on this topic.

Keywords

Derivative calculus differential equation fourier integral operator operator theory ordinary differential equation phase space pseudo-differential operator

Authors and affiliations

  • Nicolas Lerner
    • 1
  1. 1.Projet Analyse fonctionnelle Institut de Mathématique de JussieuUniversité Pierre et Marie Curie (Paris VI)Paris cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8510-1
  • Copyright Information Birkhäuser Basel 2010
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8509-5
  • Online ISBN 978-3-7643-8510-1
  • About this book
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