Contents
1. Introductio n 1
2. Representation s of SU(2) 4
3. Th e general theory of linear representations of compact groups 9
4. Li e theor y o f representation s o f compac t connecte d Li e groups.. 15
5. Induce d representations of compact groups 17
6. Spherica l functions o n compact groups 18
7. Examples ; spherical harmonics , 2 1
8. Th e general theory of spherical functions 2 5
9. Fourie r and Plancherel transforms 3 0
10. Extensio n o f th e Planchere l transfor m 3 4
11. Th e subtletie s o f harmonic analysi s 3 7
12. Differentia l propertie s o f spherica l functions o n Li e groups 4 0
13. Spherica l function s o n semisimpl e Li e groups 4 2
14. Mor e o n SL(2 , R) 4 5
15. Automorphi c function s 5 3
16. Group s o f isometrie s an d Besse l functions 5 5
17. Othe r specia l function s 5 8
References 5 9
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