Graphics Reference
In-Depth Information
for a function in
L
2
. How do you
Exercise 18.1:
(a) We defined the length
f
L
2
is finite?
know that the length of any function
f
∈
L
2
, and conclude
that the inner product of
f
and
g
is therefore always finite as well.
Exercise 18.2:
(An exercise in definitions.) Define
g
a
(
t
)=
2
a
2
2
2
=
2
(b) Show that
f
+
g
−
f
−
g
f
,
g
for any
f
,
g
∈
for
|
t
| <
a
and
0 otherwise.
(a) Show that for any function
f
:
R
→
R
,thevalue
U
(
a
)
defined in Equation
18.26 is
(
f
g
a
)(
t
0
)
.
(b) Show that the sample of
f
at
t
0
is
lim
a
→
0
(
f
g
a
)(
t
0
)
.
