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 :
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Last modified January 10, 2014.