Louis Boutet de Monvel, Selected Works

  • Victor W. Guillemin
  • Johannes Sjöstrand

Part of the Contemporary Mathematicians book series (CM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Victor W. Guillemin, Johannes Sjöstrand
    Pages 1-4
  3. Anne Boutet de Monvel
    Pages 5-16
  4. G. Grubb
    Pages 19-235
  5. T. Kawai
    Pages 237-374
  6. B. Helffer
    Pages 375-481
  7. C. L. Epstein
    Pages 483-583
  8. V. W. Guillemin
    Pages 585-713
  9. A. Weinstein
    Pages 715-774
  10. G. Lebeau
    Pages 775-847
  11. Victor W. Guillemin, Johannes Sjöstrand
    Pages 849-850
  12. Back Matter
    Pages 851-852

About this book

Introduction

This book features a selection of articles by Louis Boutet de Monvel and presents his contributions to the theory of partial differential equations and analysis. The works selected here reveal his central role in the development of his field, including three cornerstones: firstly, analytic pseudodifferential operators, which have become a fundamental aspect of analytic microlocal analysis, and secondly the Boutet de Monvel calculus for boundary problems for elliptic partial differential operators, which is still an important tool also in index theory. Thirdly, Boutet de Monvel was one of the first people to recognize the importance of the existence of generalized functions, whose singularities are concentrated on a single ray in phase space, which led him to make essential contributions to hypoelliptic operators and to a very successful and influential calculus of Toeplitz operators with applications to spectral and index theory.

Other topics treated here include microlocal analysis, star products and deformation quantization as well as problems in several complex variables, index theory and geometric quantization. This book will appeal to both experts in the field and students who are new to this subject.

Keywords

index theory pseudodifferential operators quantization spectral theory Toeplitz operators

Editors and affiliations

  • Victor W. Guillemin
    • 1
  • Johannes Sjöstrand
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institut de mathématiques de BourgogneUniversité de BourgogneDijonFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27909-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27907-7
  • Online ISBN 978-3-319-27909-1
  • About this book