1. Show that there exists a linear continuous form oon L ([0, 1]) such that o(f) = f(0) if f is continuous. 2. Using Riemann-Lebesgue Lemma, show that there is not exists any g € L¹([0,1]) such that (f) = f(t)g(t)dt for all ƒ € L∞ ([0, 1]). 3. What you can deduce from the previous parts. Good Luck
1. Show that there exists a linear continuous form oon L ([0, 1]) such that o(f) = f(0) if f is continuous. 2. Using Riemann-Lebesgue Lemma, show that there is not exists any g € L¹([0,1]) such that (f) = f(t)g(t)dt for all ƒ € L∞ ([0, 1]). 3. What you can deduce from the previous parts. Good Luck
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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part 2 3rieman lebesgue lemma part 2
![Problem 4.
1. Show that there exists a linear continuous form oon L ([0, 1]) such that o(f) = f(0)
if f is continuous.
2. Using Riemann-Lebesgue Lemma, show that there is not exists any g € L¹([0, 1])
such that (f) = f(t)g(t)dt for all f € L∞ ([0,1]).
3. What you can deduce from the previous parts.
Good Luck](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13032172-d002-48c5-a8a1-534065d0933a%2Fa33ae97e-ce25-440c-9137-b975a7113326%2Fvenxee_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4.
1. Show that there exists a linear continuous form oon L ([0, 1]) such that o(f) = f(0)
if f is continuous.
2. Using Riemann-Lebesgue Lemma, show that there is not exists any g € L¹([0, 1])
such that (f) = f(t)g(t)dt for all f € L∞ ([0,1]).
3. What you can deduce from the previous parts.
Good Luck
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