By Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M.

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**Example text**

N °I. ~ a normalization of the Haar measure on Y~U, U, V. such that Z ycG, f~(Y" Y) = In(Y)l-I ~z ~(yu-l' u Y)au We calculate f using 6). In what follows m G , ~ Z , ~ U . ~ are forms of the highest degree on G,Z etc. which define oorrespondhng Haar or Lebesgue measures. Cle~rly it is enough to prove (i0) with G X U. y=l. We shall calculate action of u cZ on V Let u = (~GXU/~) with its action be invariant under this action of the map u~ multiple cI~(Y)I -I, Let X'c2, Y'. (u,u -I "Y) e(Y)u Z. c Z.

M' of (l,Uo) such that E ~his means that we can find an analytic assignment 25 E and of 24 U ~ D'u c TI~ I u) (A × U) defined on a n o p e n n e i g h b o r h o o d Since that struction~ we assume U = U. ) , ( A x U ) ~-- N ® Tu U)~ we may identify these two spaces and so obtain an analytic assignment u ~ D'C u ~(r) ® T(r)(U)u (u c U)~ s~ch that (d~)l~lu)(D~) = D (u c U). U Suppose now D differential operator on is invariant under A× U A and let ~ determined by the assignment be the analytic D(x,u ) = D' U ((x,u) c A × U).

If E on N -i let (suppT), If order(T)