14. V. Guillemin and S. Sternber g

therefore , by the induction hypothesis is of the form p, , . We thus have

(2. 13) Trk_1 °|( = ^ , »ir;

k

k-1 "k-1 '

In orde r to establish that ij) - p, it suffices to show that for any

(2.14) 0 ( p )

# v

= j

k

(cp)(x).p. v .

We procee d as in the cas e k = 1 . Choose £ £ T (D (0;M))

P

K

with i r ^ a " ^ = p,,v . Then 4ak = v . By (2. 8),

v = i/j;!c!,ak = i M p ^ T r ^ a "

1

^ ! )

Fo r any fj € T (D,(0;M)) it follows directl y from the definitions that

Thus

v = 4)(p);~ Tr

k - 1

0 ^ ( ^ £ ) = ij){p)I O^_1((Trk-1);,c0;:^;

= 0(P)* «" ( ^ k - r ^ k - i ^ * ^ '

i/)(p)*v = a" ( ^ k - i ^ k - i M )

By (2. 6) (with k replace d by k - l) this implies (2. 14)