Exercises about Distributions

Question

I'm looking for references (books or pdf) about the following themes (especially the first two) :

1. Fourier Series of Distributions.
2. Distributional solutions of ordinary differential equations.
3. Fourier Transform of Distributions.
4. Convolution of Distributions.
5. Tempered Distributions.

with exercises (with answers) : direct applications of the theory, simple problems with detailed questions.

Thank you a lot.

Answer 1

Perhaps you could try

Claude Zuily, Problems in Distributions and Partial Differential Equations (North-Holland 1988).

Another book that might be of interest for you is

Duistermaat J., Kolk J. Distributions: Theory and Applications (Birkhäuser 2010).

Solutions to selected (starred) problems are given at the end of the book.