**Final Projects**

Tuesday Nov 26, 2013

Tuesday Dec 3, 2013

**Homework 10 ***LAST*** (due Thursday Nov 14, 2013)**

Exercise 9.22 (show Shannon function is a wavelet),

Find the Shannon Multiresolution Analysis (it
can be described completely like the Haar multiresolution analysis):
Exercises: 10.6 (see Example 10.5) and 10.39 (see Example 10.38).

*Reading assignment:* Chapter 9: Sections 9.3, and
Chapter 10: Section 10.1, 10.2 and 10.4.

**Homework 9 (due Thursday Oct 31, 2013)**

Exercise 8.26 (Time frequency dictionary for tempered distributions),

Exercise 8.33 (approximations of the identity converge to the delta
distribution).

*Reading assignment:* Chapter 8.

** Homework 8 (due Tuesday October 22, 2013):**

Work individually or in groups as you please:

Exercises 7.11, 7.13, 7.19 and 7.20 (use the inversion formula (Theorem
7.28 in Section 7.6 to show (j) )

*Reading assignment:* Chapter 7.

** Homework 7 (due Thursday 10/10/2013):**

Work individually or in groups, do only one of the following (I would like
some of you to choose the first, some of you to choose the second,
you are welcome to try both but it is not needed):

** Homework 6 (due Tuesday 10/01/2013):**

Work individually or in groups, do only one of the following:

**
Homework 5 (due Tuesday 9/24/2013):**

You are welcome to work in groups of two, same as last time,
or you may switch around:

Exercise 4.16 [note there are two typos in the Hint: k > 0 (or k >= 1),
and k=1 (instead of k=0)], Exercises 4.37 and for the computer inclined 4.40
for the Poisson kernel.

*Reading assignment:* Sections 4.2 and 4.5.

**
Homework 4 (due Thursday 9/12/2013):**

Exercises 4.5 (you can provide numerical evidence by reproducing
Figure 4.2), and 4.30 (closed formula for the Fejer Kernel).

This is group work, how about the following teams?

**
Homework 3 (due Thursday after Labor Day 9/5/2013):**

Exercise 3.18, and 3.25.
Do either 3.19 or prove that uniform convergence preserves continuity
(Theorem 2.59).

*Reading assignment:* Chapter 3.

**
Homework 2 (due Thursday 8/29/13):**

Chapter 3 - 3.1, 3.11.

*Reading assignment:* Sections 2.2 and 2.3, and Chapter 3.

**Homework 1 (due 8/22/13) :**

Chapter 1 - 1.2, 1.13.

*Reading assignment:* Chapter 1.

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: August 22, 2013