MATH 322 Harmonic Analysis
Homework # 8
Due Friday, March 30.
- Read Chapter 5, Sections 2 & 3. Do Exercises #11 -- 19. Hand in
#11, 12, 13, & 15.
Write up your results carefully.
Here are some comments on the exercises.
- Exercise 11. We have done estimates like this in class.
- Exercise 12. This example illustrates the importance of
continuity up to t = 0 in the uniqueness theorem.
- Exercise 13. The proof here is very similar to the one I did in
class.
- Exercise 14. A fairly straight forward application of Poisson
summation.
- Exercise 15. Another fairly straight forward application of
Poisson summation.
- Exercise 16. Another fairly straight forward application of
Poisson summation.
- Exercise 17. An interesting exercise if you have not already seen
it.
- Exercise 18. A straight forward verification.
- Exercise 19. This is a little harder. Just use the geometric
series wherever you can.