Advertisement

Pseudo-Differential Operators and Symmetries

Background Analysis and Advanced Topics

  • Michael Ruzhansky
  • Ville Turunen

Part of the Pseudo-Differential Operators book series (PDO, volume 2)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Michael Ruzhansky, Ville Turunen
      Pages 1-6
  3. Foundations of Analysis

    1. Front Matter
      Pages 7-7
    2. Michael Ruzhansky, Ville Turunen
      Pages 9-78
    3. Michael Ruzhansky, Ville Turunen
      Pages 79-113
    4. Michael Ruzhansky, Ville Turunen
      Pages 115-189
    5. Michael Ruzhansky, Ville Turunen
      Pages 191-218
  4. Commutative Symmetries

    1. Front Matter
      Pages 219-220
    2. Michael Ruzhansky, Ville Turunen
      Pages 221-258
    3. Michael Ruzhansky, Ville Turunen
      Pages 259-296
    4. Michael Ruzhansky, Ville Turunen
      Pages 297-331
    5. Michael Ruzhansky, Ville Turunen
      Pages 333-412
    6. Michael Ruzhansky, Ville Turunen
      Pages 413-426
  5. Representation Theory of Compact Groups

    1. Front Matter
      Pages 427-427
    2. Michael Ruzhansky, Ville Turunen
      Pages 429-444
    3. Michael Ruzhansky, Ville Turunen
      Pages 445-489
    4. Michael Ruzhansky, Ville Turunen
      Pages 491-513
    5. Michael Ruzhansky, Ville Turunen
      Pages 515-526
  6. Non-commutative Symmetries

    1. Front Matter
      Pages 527-528
    2. Michael Ruzhansky, Ville Turunen
      Pages 529-593
    3. Michael Ruzhansky, Ville Turunen
      Pages 595-630
    4. Michael Ruzhansky, Ville Turunen
      Pages 631-665
    5. Michael Ruzhansky, Ville Turunen
      Pages 667-681
  7. Back Matter
    Pages 683-709

About this book

Introduction

This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.

Keywords

Lie group algebra homogeneous space manifold pseudo-differential operator quantization torus

Authors and affiliations

  • Michael Ruzhansky
    • 1
  • Ville Turunen
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Institute of MathematicsHelsinki University of TechnologyFinland

Bibliographic information

Industry Sectors
Pharma
Finance, Business & Banking
Electronics
Aerospace
Oil, Gas & Geosciences