2. Let V R(0, 27]) be the space of Riemann integrable functions, with the usual inner product 27T -da f (x)9(x) 2T (f,g) If A C [0, 27T, recall XA(x) is the indicator function on A, that is, if x E A XA(x) if xA Then if f E V, the product fxA(x) is given by fxA() (x) if r E A; 10 if A (a) Let f(a) (b) Let A [0, 1], and define h(x) = f(x)XA(x). Give h explicitly give f h explicitly = x. Show that fE R(0, 27) by computing its norm piecewise function. Then as a piecewise function as a
2. Let V R(0, 27]) be the space of Riemann integrable functions, with the usual inner product 27T -da f (x)9(x) 2T (f,g) If A C [0, 27T, recall XA(x) is the indicator function on A, that is, if x E A XA(x) if xA Then if f E V, the product fxA(x) is given by fxA() (x) if r E A; 10 if A (a) Let f(a) (b) Let A [0, 1], and define h(x) = f(x)XA(x). Give h explicitly give f h explicitly = x. Show that fE R(0, 27) by computing its norm piecewise function. Then as a piecewise function as a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. Let V R(0, 27]) be the space of Riemann integrable functions, with the usual inner product
27T
-da
f (x)9(x)
2T
(f,g)
If A C [0, 27T, recall XA(x) is the indicator function on A, that is,
if x E A
XA(x)
if xA
Then if f E V, the product fxA(x) is given by
fxA() (x) if r E A;
10
if A
(a) Let f(a)
(b) Let A [0, 1], and define h(x) = f(x)XA(x). Give h explicitly
give f h explicitly
= x. Show that fE R(0, 27) by computing its norm
piecewise function. Then
as a
piecewise function
as a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F236988f8-663b-4ed3-ac92-83ca95944bca%2F6bf4aaa4-a44f-42b7-8d1a-7a871695ce6b%2Fxgk2c9.png&w=3840&q=75)
Transcribed Image Text:2. Let V R(0, 27]) be the space of Riemann integrable functions, with the usual inner product
27T
-da
f (x)9(x)
2T
(f,g)
If A C [0, 27T, recall XA(x) is the indicator function on A, that is,
if x E A
XA(x)
if xA
Then if f E V, the product fxA(x) is given by
fxA() (x) if r E A;
10
if A
(a) Let f(a)
(b) Let A [0, 1], and define h(x) = f(x)XA(x). Give h explicitly
give f h explicitly
= x. Show that fE R(0, 27) by computing its norm
piecewise function. Then
as a
piecewise function
as a
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