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$L^{p}$ harmonic analysis on $SL(2,R)$
About this Title
William H. Barker
Publication: Memoirs of the American Mathematical Society
Publication Year:
1988; Volume 76, Number 393
ISBNs: 978-0-8218-2456-6 (print); 978-1-4704-0813-8 (online)
DOI: https://doi.org/10.1090/memo/0393
MathSciNet review: 946617
MSC: Primary 22E30; Secondary 22E46
Table of Contents
Chapters
- 1. Introduction
- 2. Notation and preliminaries
- 3. The $L^p$ Schwartz spaces
- 4. The principal series
- 5. The discrete series
- 6. Leading exponents and distributions
- 7. Relationships between principal and discrete series matrix coefficients
- 8. The Trombi-Varadarajan estimates for $\textrm {SL}(2, \mathbb {R})$
- 9. The Fourier transform on $\mathcal {C}^p(G)$
- 10. The Plancherel inversion formula
- 11. The decomposition of $\mathcal {C}^p(G)$
- 12. Asymptotic approximation of matrix coefficients
- 13. Growth of asymptotic coefficients for the principal series
- 14. Calculation of asymptotic coefficents for the discrete series
- 15. The inverse transform
- 16. The isomorphism theorem: Non-integral case
- 17. The Campoli functions
- 18. The isomorphism theorem: General case
- 19. The zero-Schwartz space (with Henrik Schlichtkrull)