Solution 2.9.2.9
f(t)=A[1(t);1(t ;T
1
)]+B [1(t; T
1
);1(t ;T
2
)]+C [1(t; T
2
);1(t ;T
3
)]
Then
F(s) = LfA1(t)g;LfA1(t; T
1
)g+ LfB1(t ;T
1
)g;LfB1(t ;T
2
)g
+LfC1(t ;T
2
)g;LfC1(t ;T
3
)g
=
A
s
;
Ae
;T
1
s
s
+
Be
;T
1
s
s
;
Be
;T
2
s
s
+
Ce
;T
2
s
s
;
Ce
;T
3
s
s
=
A(1;e
;T
1
s
)B(e
;T
1
s
; e
;T
2
s
)+C(e
;T
2
s
; e
;T
3
s
)
s
1
