MATH 322 Harmonic Analysis

Due Friday, February 23.

• Read the Problems starting on p.65. Do #2 and hand it in.
• Read Chapter 3. Do Exercises 3 -- 9, 13, & 14. Hand in #3, 6, 7, & 14.

Here are some comments on the exercises

• Exercise 3. Read the Hint.
• Exercise 4. We discussed this in class to some extent.
• Exercise 5. We discussed a similar example in class.
• Exercise 6. Look at the Abel means of the series.
• Exercise 7. The Dirichlet test might be helpful.
• Exercise 8. A nice exercise in the use of Parseval's identity.
• Exercise 9. A nice exercise in the use of Parseval's identity.
• Exercise 13. Easy.
• Exercise 14. This result is an important improvement on our previously best convergence theorem. However, it is not as good as Bernstein's Theorem, stated in Exercise 16, which is part of your first project. The hint says to use Cauchy-Schwarz. To do so you might notice that f^(n) = (1/n)(nf^(n)).