6 BEL A SZ.-NAGY
Because o f (1.3.1) w e therefor e hav e
(1.4.7) Q * = U ~ UT*)§.
As M
+
(Q) i s invarian t fo r U
+ i
it s orthogona l complemen t i n ft
+
, tha t i s § , i s
invariant fo r L /
+
. A s b y th e dilatio n propert y w e hav e P^U
+
\1Q = T , w e conclud e tha t
(1.4.8) T * = tf*|§.
We clos e thi s sectio n b y observin g tha t becaus e o f th e relation s
oo - 1
»= V u
n§=
V u
n®+
_ o o —oo
we obtain , fro m (1.4.5), th e followin g alternativ e decompositio n o f ft:
d.4.9) ft = AKC^) e s t
We shal l us e th e abov e decomposition s o f th e space s ft
+
an d ft, an d th e relatio n
(1.4.8) betwee n T an d U
+
t o construc t a functiona l mode l fo r T .
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