AMREIN BOUTET DE MONVEL-BERTHIER GEORGESCU
(Pv,[MhJ-M'h -2h M]Pv) + (v,(h£M)fv) ,
2Im((h
1
P+ih
o
)v,2iMcp
T
Pv+[(Mcp
t
)
f
- M i p
| 2
] v ) =
= ( P v ^ h ^ ' M P v ) + 2Im(v,2h
o
cp'MPv) +
+ 2Im(Pv
s
h
1
[(^4cp
,
)
f
-Mcp
, 2
]v ) - 2 ( v , h [
(Mcp1
)
f -Mcp1 2
] v )
- (Pv,4h
1
(p
!
MPv) + (v,(2h
o
cp
f
M)
f
v ) + 2 I m ( P v , h
1
(M(p!
)
f
v ) +
+ ( v , ( h
1
M c p
, 2
)
f
v ) - 2(v
3
h
o
[(M(p
f
)
f
-Mcp'
2
]v ) =
(Pv
3
4h
1
cp'MPv) + 2Im(Pv,h
1
(Ivi T (p f +Mpf,)v) +
( v J C h ^ l t p '
2
) ' + 2(h
o
p'M)
T
-2h
o
(M(p' + 2h
Q
Mcp
, 2
]v)
In this paper we shall use only a very special case of the identity
(2.12) . For K G 3R we set
(2.13) PK = P - ift
By taking h (t) = t and h (t) = -|(a-l) in (2.12) and using the defi-
nition (2.7) , we obtain :
p
Corollary 2.4 (Fundamental Identity ) : If a G 3R , t p C (I) and v G V ,
then
2Im(P1_av,tL(cp)v) = (v, [(2-a)PMP+Q ]v) +
+ (Pv,[4Mttp,-tMt ]Pv) + (v,[M(a+t|^-)tp,2+tM'cpt2]v) +
(2.14) + 2Im(Pv,tMfip'v) + 2Im(Pv,tMq"v) +
+ 2Im(P1_av,t(SP+R+i(p!S)v)
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