Homework 5

tags: 224a

Due 11/21
Problems may be added until 11/14.

1. Dimock Problem 1.4
2. Dimock Problem 1.6
3. Dimock Problem 1.9
4. Dimock Problem 1.15
5. Dimock Problem 4.3
6. Dimock Problem 4.5
7. Dimock Problem 4.6
8. Dimock Problem 4.7
9. Prove that if
   $T\in {\mathcal{S}}^{\prime }(R)$ then there exist
   $C,k,m$ such that
   
   $$|T(\varphi )|\le C\Vert \varphi {\Vert }_{k,m},$$
   for every Schwartz function
   $\varphi \in \mathcal{S}(R)$.
10. Reed and Simon V.30
11. Calculate the fundamental solution of the Poisson equation
    $\mathrm{\Delta }u=f$ in
    ${\mathbb{R}}^3$ using the Fourier transform.