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§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP

  • Peter D. Lax and Ralph S. Phillips
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Scattering Theory for Automorphic Functions. (AM-87), Volume 87
This chapter is in the book Scattering Theory for Automorphic Functions. (AM-87), Volume 87
© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. PREFACE vii
  4. LIST OF SYMBOLS ix
  5. §1. INTRODUCTION 1
  6. §2. AN ABSTRACT SCATTERING THEORY 12
  7. §3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM 53
  8. §4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP 87
  9. §5. THE AUTOMORPHIC WAVE EQUATIONS 102
  10. §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION 119
  11. §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION 149
  12. §8. THE GENERAL CASE 191
  13. §9. THE SELBERG TRACE FORMULA 220
  14. REFERENCES 297
  15. INDEX 299
  16. Backmatter 301
https://doi.org/10.1515/9781400881567-006

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. PREFACE vii
  4. LIST OF SYMBOLS ix
  5. §1. INTRODUCTION 1
  6. §2. AN ABSTRACT SCATTERING THEORY 12
  7. §3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM 53
  8. §4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP 87
  9. §5. THE AUTOMORPHIC WAVE EQUATIONS 102
  10. §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION 119
  11. §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION 149
  12. §8. THE GENERAL CASE 191
  13. §9. THE SELBERG TRACE FORMULA 220
  14. REFERENCES 297
  15. INDEX 299
  16. Backmatter 301
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