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§4. THE METAPLECTIC REPRESENTATION

  • L. Boutet de Monvel and Victor Guillemin
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The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99
This chapter is in the book The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99
© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. §1. Introduction 1
  4. §2. GENERALIZED TOEPLITZ OPERATORS 11
  5. §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE 21
  6. §4. THE METAPLECTIC REPRESENTATION 27
  7. §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS 35
  8. §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES 39
  9. §7. THE COMPOSITION THEOREM 44
  10. §8. THE PROOF OF THEOREM 7.5 51
  11. §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS 66
  12. §10. THE TRANSPORT EQUATION 77
  13. §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS 80
  14. §12. THE TRACE FORMULA 90
  15. §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS 99
  16. §14. THE HILBERT POLYNOMIAL 110
  17. §15. SOME CONCLUDING REMARKS 123
  18. BIBLIOGRAPHY 128
  19. APPENDIX: QUANTIZED CONTACT STRUCTURES 131
  20. Backmatter 161
https://doi.org/10.1515/9781400881444-004

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. §1. Introduction 1
  4. §2. GENERALIZED TOEPLITZ OPERATORS 11
  5. §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE 21
  6. §4. THE METAPLECTIC REPRESENTATION 27
  7. §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS 35
  8. §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES 39
  9. §7. THE COMPOSITION THEOREM 44
  10. §8. THE PROOF OF THEOREM 7.5 51
  11. §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS 66
  12. §10. THE TRANSPORT EQUATION 77
  13. §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS 80
  14. §12. THE TRACE FORMULA 90
  15. §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS 99
  16. §14. THE HILBERT POLYNOMIAL 110
  17. §15. SOME CONCLUDING REMARKS 123
  18. BIBLIOGRAPHY 128
  19. APPENDIX: QUANTIZED CONTACT STRUCTURES 131
  20. Backmatter 161
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