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Preface Introduction Part ¢ñ.Fourier transforms on the Lie algebra 1.The mapping f¡ú?^f 2.Some results about nei***orhoods of semisimple elements 3.Proof of Theorem 3.1 4.Some consequences of Theorem 3.1 5.Proof of Theorem 5.11 6.Application of the induction hypothesis 7.Reformulation of the problem and completion of the proof 8.Some results on Shalika's germs 9.Proof of Theorem 9.6 Part ¢ò.An extension and proof of Howe's Theorem 10.Some special subsets of g 11.An extension of Howe's Theorem 12.First step in the proof of Howe's Theorem 13.Completion of the proof of Howe's Theorem Part ¢ó.Theory on the group 14.Representations of compact groups 15.Admissible distributions 16.Statement of the main results 17.Recapitulation of Howe's theory 18.Application to admissible invariant distributions 19.First step of the reduction from G to M 20.Second step 21.Completion of the proof 22.Formal degree of a supercuspidal representation Bibliography List of Symbols Index