Course Documents

Homework Assignments

• Homework 1, due Tuesday 3/17/09: Read chapter 1, do and turn in problems 3, 6, 10, and 11.
• Homework 2, due Friday 3/27/09: Read chapter 2, do and turn in problems 1, 3, 7, 13, 17, 19.
• Homework 3, due Friday 4/10/09: Read chapter 3, do and turn in problems 2, 6, 7, 10, 11. Also, show that if a function f(x) on the reals has compact support and is "n" times continuously differentiable then the quantity y^n*F(y) (where F is the Fourier transform of f) remains bounded as y goes to plus or minus infinity. (Thus the smooth f is, the faster its Fourier transform decays.)
• Homework 4, due Friday 4/24/09: Read chapter 5, do and turn in problems 1, 3, 4, 7. Also do an turn in these rather concrete problems.
• Homework 5, due Monday 5/4/09: Read chapter 6, do and turn in problems 6.4, 6.6, 6.8, 6.10, 6.15, 6.19.
• Homework 6, due Monday 5/11/09: Read chapter 7, do and turn in problems 7.1, 7.2, 7.3, 7.6.
• Homework 7, due Thursday 5/21/09: Read chapter 8, do and turn in problems 8.1, 8.2, 8.4, 8.5. Also, do the following problem: Show that Rn (euclidean n-space) is an LCA group, with vector addition as the group operation. Write out what the characters on Rn look like, as well as the forward and inverse Fourier transform on Rn. (Feel free to use Lemma 8.4.3 under the assumption that A is uncountable.)