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)
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