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Coherent States, Wavelets and Their Generalizations

  • Textbook
  • © 2000

Overview

Authors:
  1. Syed Twareque Ali

    1. Department of Mathematics and Statistics, Concordia University Loyola Campus, Montréal, Canada

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  2. Jean-Pierre Antoine

    1. Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

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  3. Jean-Pierre Gazeau

    1. Laboratoire Physique Théoretique and Matière Condensée, Université de Paris 7 — Denis Diderot, Paris, France

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Part of the book series: Graduate Texts in Contemporary Physics (GTCP)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 1-12

  3. Canonical Coherent States

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 13-32

  4. Positive Operator-Valued Measures and Frames

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 33-45

  5. Some Group Theory

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 47-87

  6. Hilbert Spaces with Reproducing Kernels and Coherent States

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 89-108

  7. Square Integrable and Holomorphic Kernels

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 109-125

  8. Covariant Coherent States

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 127-145

  9. Coherent States from Square Integrable Representations

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 147-170

  10. Some Examples and Generalizations

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 171-197

  11. CS of General Semidirect Product Groups

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 199-223

  12. CS of the Relativity Groups

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 225-256

  13. Wavelets

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 257-282

  14. Discrete Wavelet Transforms

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 283-305

  15. Multidimensional Wavelets

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 307-330

  16. Wavelets Related to Other Groups

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 331-351

  17. The Discretization Problem: Frames, Sampling, and All That

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 353-387

  18. Conclusion and Outlook

    • Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
    Pages 389-391

  19. Back Matter

    Pages 393-418
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About this book

Nitya kaaler utshab taba Bishyer-i-dipaalika Aami shudhu tar-i-mateer pradeep Jaalao tahaar shikhaa 1 - Tagore Should authors feel compelled to justify the writing of yet another book? In an overpopulated world, should parents feel compelled to justify bringing forth yet another child? Perhaps not! But an act of creation is also an act of love, and a love story can always be happily shared. In writing this book, it has been our feeling that, in all of the wealth of material on coherent states and wavelets, there exists a lack of a discern­ able, unifying mathematical perspective. The use of wavelets in research and technology has witnessed explosive growth in recent years, while the use of coherent states in numerous areas of theoretical and experimental physics has been an established trend for decades. Yet it is not at all un­ common to find practitioners in either one of the two disciplines who are hardly aware of one discipline's links to the other. Currently, many books are on the market that treat the subject of wavelets from a wide range of perspectives and with windows on one or several areas of a large spectrum IThine is an eternal celebration '" A cosmic Festival of Lights! '" Therein I am a mere flicker of a wicker lamp, , . 0 kindle its flame (my Master!), vi Preface of possible applications.

Reviews

From the reviews:

"The subject of coherent states and/or wavelets (CS-W) is a hot topic for decades. … Personally I prefer the book under review to many other ones published before. … It is clearly written, mathematically sound and well illustrated … . Short but informative historical remarks in the text additionally guide through the literature. The index is useful too. … I recommend this book to everyone who wishes to learn CS-W, or already works in the area, or just needs a good reference source." (Vladimir V. Kisil, Zentralblatt MATH, Vol. 1064, 2005)

Authors and Affiliations

  • Department of Mathematics and Statistics, Concordia University Loyola Campus, Montréal, Canada

    Syed Twareque Ali

  • Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  • Laboratoire Physique Théoretique and Matière Condensée, Université de Paris 7 — Denis Diderot, Paris, France

    Jean-Pierre Gazeau

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