MATH 322 Harmonic Analysis

Due Friday, February 2.

Read Chapter 2 pp 29 -- 44. Do Exercises 1 -- 8 starting on p. 58. Turn in solutions to Exercises 6, 7, & 8. Write them up carefully.

Here are some comments on the exercises

• 1. I essentially did this one in class.
• 2. You should be aware of this transfer between exponential and trig notation.
• 3. You are to compute the Fourier series for the function defined on p. 17 and illustrated in Figure 8.
• 4 -- 6 are routine. Since 6 has some interesting features you are asked to turn that one in.
• 7. The Dirichlet test is very useful in this subject so you should learn it. You may have seen it in Math 321. I believe it is an exercise in Rudin.
• 8. This is a typical application of the Dirichlet test. Notice that the series does not converge absolutely. A glance at the Dirichlet kernel defined in Example 4 on p. 37 might be helpful.