MATH 322 Harmonic Analysis

Due Friday, February 9.

Read Chapter 2. Do Exercises 9 -- 20 starting on p. 61. Turn in solutions to Exercises 9, 13, 16, & 19. Write them up carefully.

Here are some comments on the exercises

• 9. Parts of this problem are very like # 8, which you did last week.
• 10, 12, & 15. Done in class.
• 11. Like proofs done in class.
• 13. This exercise describes the relationships between convergence and the two forms of summability we have discussed.
• 14. This exercise compliments #13. Do not work too hard on this if you do not see the proof.
• 16. This is a useful and important result. You should remember it.
• 17. We have discussed what happens to Fourier series at points where the function is continuous. What about points of discontinuity?
• 18. Here is an interesting example. Why doesn't it contradict Theorem 5.7?
• 19. This should remind you of the first homework assignment, and Theorem 5.7.
• 20. Another example like Theorem 5.7 and Exercise 19.