Assignment 1: Exercises 2, 4, 6, 7, 8 on pages 59-61. |
Assignment 2: Exercises 12, 13, 14, 19 on pages 62-64. |
Assignment 3: Exercises 12, 13, 14, 15 on pages 91-92. |
Assignment 4: Exercises 11, 12, 13, 15, 23 on pages 164-169. |
Assignment 5: Exercises 4, 7, 8, and Problem 3, on pages 208-214. |
Assignment 6: Exercises 5, 6, 10 on pages 209-211. |
Assignment 7: All the exercises of the notes on distributions. |
Assignment 8: Exercises 3, 4, 5, 6, 13 on pages 236-239. |
References:
The main reference is Fourier Analysis of E.M. Stein and R. Shakarchi, Princeton, 2003. The assignments above refer to this book. But the following references are very much worth studying:G. Frieseke, Lectures on Fourier Analysis, 2007.
A. Pinkus and S. Zafrany, Fourier Series and Integral Transforms, Cambridge, 1997.
G.B. Folland, Real Analysis, Wiley, 1999.
E.H. Lieb and M. Loss, Analysis, AMS, 2001.
J.K. Hunter and B. Nachtergaele, Applied Analysis, World Scientific, 2001. (This book is available online.)
M. Reed and B. Simon, Fourier Analysis, Self-Adjointness (Methods of Modern Mathematical Physics II), Elsevier, 1975.