Math 8370, Harmonic Analysis 1
Semester 1, 2024-2025
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Office: Math 227
Email: packer@colorado.edu
URL: http://math.colorado.edu/~packer
Course Syllabus: For course syllabus, click here!
Course Information:
The material covered will include most of Chapters 1, 2, and 3, and part of
Chapter 6, 7 and 10 in the Dietmar textbook listed below. These topics include:
Topics to be covered include: A review of periodic functions on the real line,
relating them to functions on the unit circle, trigonometric polynomials and Fourier series on the circle,
including convergence problems for Fourier series on the unit circle including convergence in L^1 and L^2$ mean,
pointwise and absolute convergence. Convolution in L^1(T). 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 Poisson Summation formula. Depending on student interest we might cover one or
more of the following topics: Theta series, Fourier analysis on locally compact abelian groups and Pontryagin
duality; representation theory for the matrix group $SU(2),$ and/or representation theory for the Heisenberg group.
Prerequisite:
Math 6320, or instructor consent.
Course Text:
We will use the text "A First Course in Harmonic Analysis" Second Edition, by Anton Dietmar,
Universitext, Springer, New York, NY, 2005,
covering much of the first half of the book. This book is available in the CU bookstore, and
an e-copy can be downloaded from the CU library.
Assessment:
- Homework Assignments (every two to three weeks or so): 40 % ; I will drop your lowest score.
- Attendance and Homework participation: 10 % of your final grade will be come from your attendance
and participation in presenting homework problems from time to time.
- Final oral and written project on topic related to
functional analysis, written version due December 15, 2024: 50 % .
Lecture Hours and Venue:
MWF 10:10 a.m.- 11:00 p.m. , MATH 220.
Final Exam Period:
Our final examination period is scheduled for Sunday, December 15, 2024, 7:30 p.m. to 10 p.m. Keep this
time free to give or listen to oral project presentations.
Office Hours:
MWF 11:10 - 12:10 p.m., MATH 227, and by appointment via ZOOM.
Important University Rules and Regulations: Click HERE
for all the important university rules and regulations that must be listed on syllabi.
Some Important Names associated with Harmonic Analysis :
S. Banach
A. Cauchy
J. Fourier
D. Hilbert
M. Frechet
I. Gelfand
H. Hahn
L. Schwartz
S. Sobolev
M. Stone
J. von Neumann
K. Weierstrass
Back to the home page of Judith A. Packer
Last modified August 14, 2024.