Math 8370, Harmonic Analysis 1
Spring Semester 2, 2017-18
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:
We will cover all of Chapters 1 - 3 of the Deitmar textbook, and in addition, potential material from Chapters 6, 7, 10 and 11. 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 studying some of the following topics: locally compact abelian groups and Pontryagin duality, representation theory for SU(2), 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" by A. Deitmar, Second Edition, Springer Verlag, 2005 covering most of Chapters 1 - 3 and parts of Chapter 6, 7 , 10 and 11,
depending on student and instructor interest.
We will also use as references the book"An Introduction to Fourier Analysis and Wavelets" by M. Pinksy, American Math. Society, 2002.
Assessment:
- Homework Assignments (every three weeks or so): 65 %
- Final project on topic related to
harmonic analysis, due early May: 35 % . This involves a written paper and an oral presentation, so please reserve the exam period
for our course, Sunday, May 6, 2018, 1:30 p.m.-4 p.m. for presentations (both giving them and listening to them).
Lecture Hours and Venue:
MWF 10 a.m.-10:50 a.m. ECCR 118.
Office Hours:
MWF 2-3 p.m., and by appointment.
Homework:
- Assignment 1, due Wednesday, January 31
- Assignment 2, due Friday, February 16
- Assignment 3, due Wednesday, March 14
- Assignment 4, due Monday, April 9
- Assignment 5, due Monday, April 23
Some Important Names associated with Harmonic Analysis :
Back to the home page of Judith A. Packer
Last modified January 15, 2018.