Wavelet Transforms and Localization Operators

  • M. W. Wong

Part of the Operator Theory: Advances and Applications book series (OT, volume 136)

Table of contents

  1. Front Matter
    Pages i-vii
  2. M. W. Wong
    Pages 1-10
  3. M. W. Wong
    Pages 11-20
  4. M. W. Wong
    Pages 21-24
  5. M. W. Wong
    Pages 25-33
  6. M. W. Wong
    Pages 34-38
  7. M. W. Wong
    Pages 39-47
  8. M. W. Wong
    Pages 48-50
  9. M. W. Wong
    Pages 51-52
  10. M. W. Wong
    Pages 53-56
  11. M. W. Wong
    Pages 57-59
  12. M. W. Wong
    Pages 60-62
  13. M. W. Wong
    Pages 63-66
  14. M. W. Wong
    Pages 67-70
  15. M. W. Wong
    Pages 71-78
  16. M. W. Wong
    Pages 84-89
  17. M. W. Wong
    Pages 90-97
  18. M. W. Wong
    Pages 98-106
  19. M. W. Wong
    Pages 107-112
  20. M. W. Wong
    Pages 113-116
  21. M. W. Wong
    Pages 117-123
  22. M. W. Wong
    Pages 124-128
  23. M. W. Wong
    Pages 129-140
  24. M. W. Wong
    Pages 141-142
  25. M. W. Wong
    Pages 143-146
  26. M. W. Wong
    Pages 147-148
  27. Back Matter
    Pages 149-156

About this book


This book is based on lectures given at the Global Analysis Research Center (GARC) of Seoul National University in 1999and at Peking University in 1999and 2000. Preliminary versions of the book have been used for various topics courses in analysis for graduate students at York University. We study in this book wavelet transforms and localization operators in the context of infinite-dimensional and square-integrable representations of locally compact and Hausdorffgroups. The wavelet transforms studied in this book, which include the ones that come from the Weyl-Heisenberg group and the well-known affine group, are the building blocks of localization operators. The theme that dominates the book is the spectral theory of wavelet transforms and localization operators in the form of Schatten-von Neumann norm inequalities. Several chap­ ters are also devoted to the product formulas for concrete localization operators such as Daubechies operators and wavelet multipliers. This book is a natural sequel to the book on pseudo-differential operators [103] and the book on Weyl transforms [102] by the author. Indeed, localization operators on the Weyl-Heisenberg group are Weyl transforms, which are in fact pseudo-differential operators. Details on the perspective and the organization of the book are laid out in the first chapter. This is a book on mathematics and is written for anyone who has taken basic graduate courses in measure theory and functional analysis. Some knowledge of group theory and general topology at the undergraduate level is also assumed.


functional analysis harmonic analysis mathematical physics measure operator theory signal analysis wavelets

Authors and affiliations

  • M. W. Wong
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

Bibliographic information