MATH 322 Harmonic Analysis

Due Friday, February 16.

• Read the Problems starting on p.65. Do #2 and hand it in.
• Read Chapter 3. Do Exercises 1 & 2 and hand in #2.

Here are some comments on the exercises

• Problem #1. Part (a) was done in class. The other parts provide other examples of integrable functions with lots of discontinuities.
• Problem #2. This shows that the Dirichlet kernel does not satisfy the hypotheses of the Approximation of the Identity Theorem. This fact makes the study of the convergence of Fourier series difficult.
• Exercise 1. I am sure you have seen this done in other Math classes.
• Exercise 2. The proof here is not too unlike the proof in Exercise #1.