a. Let w ( t ) be a positive-valued function in C [ a , b ] ,where b > a . Verify that the rule 〈 f , g 〉 = ∫ a b w ( t ) f ( t ) g ( t ) d t defines an inner product on C [ a , b ] . b. If we chose the weight function w ( t ) so that ∫ a b w ( t ) d t = 1 , what is the norm of the constantfunction f ( t ) = 1 in this inner product space?
a. Let w ( t ) be a positive-valued function in C [ a , b ] ,where b > a . Verify that the rule 〈 f , g 〉 = ∫ a b w ( t ) f ( t ) g ( t ) d t defines an inner product on C [ a , b ] . b. If we chose the weight function w ( t ) so that ∫ a b w ( t ) d t = 1 , what is the norm of the constantfunction f ( t ) = 1 in this inner product space?
a. Let
w
(
t
)
be a positive-valued function in
C
[
a
,
b
]
,where
b
>
a
. Verify that the rule
〈
f
,
g
〉
=
∫
a
b
w
(
t
)
f
(
t
)
g
(
t
)
d
t
defines an inner product on
C
[
a
,
b
]
. b. If we chose the weight function
w
(
t
)
so that
∫
a
b
w
(
t
)
d
t
=
1
, what is the norm of the constantfunction
f
(
t
)
=
1
in this inner product space?
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