TABLE OF CONTENTS
1. Introduction 1
2. Notation and Preliminaries 7
3. The
Lp
Schwartz Spaces 13
4. The Principal Series 15
5. The Discrete Series 19
6. Leading Exponents and Distributions 23
7. Relationships between Principal and Discrete Series Matrix Coefficients 29
8. The Trombi-Varadarajan Estimates for SL(2, R) 33
9. The Fourier Transform on
CP(G)
37
10. The Plancherel Inversion Formula 46
11. The Decomposition of
CP(G)
49
12. Asymptotic Approximation of Matrix Coefficients 53
13. Growth of Asymptotic Coefficients for the Principal Series 62
14. Calculation of Asymptotic Coefficents for the Discrete Series 70
15. The Inverse Transform 76
16. The Isomorphism Theorem: Non-Integral Case 88
17. The Campoli Functions 92
18. The Isomorphism Theorem: General Case 97
19. The Zero-Schwartz Space (with Henrik Schlichtkrull) 99
List of Notation 107
References 109
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