TTh 9.00-10.20 am, 130 Lockett Hall
Syllabus
This is a basic introduction
to Fourier analysis on Rn.
It includes the theory of the Fourier transform, Fourier series, and related
topics. We will also discuss the theory of distributions, Fourier multipliers,
Calderon-Zygmund singular integrals, interpolation
theory, the Hardy-Littlewood maximal operator, and
more. Possible formats include group reading, written and oral presentations.
Prerequisites: Multidimensional
Calculus (4035), Real Analysis (7311), or equivalent.
Instructor: Boris
Rubin, borisr@math.lsu.edu, 348 Lockett Hall;
Office hours: Tuesday 3.30 – 4.30 pm and by appointment.
Texts:
1. J. Duoandikoetxea, Fourier
Analysis, AMS, 2001.
2. L. Grafakos, Classical
Fourier Analysis, Springer, 2008.
3. E.M, Stein and G.Weiss,
Introduction Fourier Analysis on Euclidean Spaces,
Princeton Univ. Press, 1971.
Grading:
The final grade will be issued according to the quality of written and
oral presentations, and the activity in class. The quality of the presentations
includes the following:
1. Complete understanding of the
material.
2. Detailed, well-organized, and
neatly-written (or typed) text of the presentation. The
text must be handed out or emailed to every participant of
the course.
3. Blackboard techniques, an eye contact
with the audience, a style of speaking during
the presentation (no garbage words,
grammatically complete sentences, etc.).
The activity in class means asking questions,
making suggestions, thinking about modifications and generalizations.
Advice:
- Be critical and doubtful- math texts may contain gaps,
typos, mistakes.
- To prepare your presentation you must be familiar with
the previous material of the course. Keep up with the class.
- Plan your time. Start preparation of your presentation
without delay. Reserve time for questions, reading auxiliary literature,
meetings with the instructor.
- Rehearse your presentation.