## Math 8370, Harmonic Analysis 1

## Spring Semester 2, 2013-14

**Course Lecturer **
#### Dr. Judith Packer, Dept. of Mathematics

*Tel: (303) 492-6979*

Office: Math 227

Email: packer@colorado.edu

URL: http://spot.colorado.edu/~packer

**Course Syllabus: For course syllabus, click here! **

**Course Information:**

The material to be covered includes some of Chapter I and most of Chapters II,
III, IV, and VI in the Katznelson book. Topics to be covered include:
A review of periodic functions and **T**,
trigonometric polynomials, and Fourier series on the circle,
including convergence problems for Fourier series on **T**, including L^1 and L^2;
mean, pointwise and absolute convergence. Convolution in L^1(**T**). Conjugate functions,
maximal functions, and Hardy spaces. An overview of interpolation of norms and linear operators;
the Hausdorff-Young theorem. The Fourier Transform in L^1(**R**): convolution in
L^1(**R**) approximate identities and the Poisson summation formula.
The Fourier transform in L^2(**R**), inversion and the Plancherel Theorem.
The course will conclude with an introduction to the wavelet transform and the Haar
wavelet expansion, the multiresolution analysis construction: scaling functions and wavelets, and
if time permits, we will finish up with a discussion of Daubechies wavelets with compact support.

**Prerequisite:**

Math 5320,or 6320, or instructor consent.

**Course Text:**

We will use the text "An Introduction to Fourier Analysis and Wavelets" by M. Pinksy, American Math. Society, 2002 covering most of Chapters 1 - 4 and parts of Chapter 6.
We will also use as references the book "An Introduction to Harmonic Analysis" by Y. Katznelson, Dover, 1976.

**Assessment:**
- Homework Assignments (every three weeks or so): 65 %
- Final project on topic related to
harmonic analysis, due early May: 35 % . There will be oral presentations, so please reserve the exam period
for our course, Tuesday, May 6, 1:30 p.m.-4 p.m. for presentations (both giving them and listening to them).

**Lecture Hours and Venue: **

MWF 1 p.m.-1:50 p.m. ECCR 118

**Office Hours: **

MWF 3-4 p.m., and by appointment.

** Homework: **

- Assignment 1, due Wednesday, January 29, 2014.
- Assignment 2, due Wednesday, February 19, 2014.
- Some solutions to problems from HW 1 and HW 2.
- Assignment 3, due Wednesday, March 12, 2014.
- Assignment 4, due Friday, April 4, 2014.
- Assignment 5, due Wednesday, April 23, 2014.

**Some Important Names associated with Harmonic Analysis :**

Back to the home page of Judith A. Packer

Last modified January 10, 2014.