Spring Semester 2006

100371 Introductory Harmonic Analysis

Links:

Handouts and problem sheets
A summary of what Harmonic Analysis is about can be found at Wikipedia .
There are many webpages telling you valuable information, e.g., the one by Mauro Maggioni has something on almost everything covered in our course.

Summary:

The core material of the course is devoted to the three pillars of classical Harmonic Analysis: Fourier series on the torus, Fourier transforms on Euclidean spaces, and Harmonic Analysis on locally compact Abelian groups. In the remaining time, an introduction to real-variable methods (maximal functions, Hilbert transform, singular integrals), and/or to the basics of time-frequency analysis, wavelets, and frames will be given.

Reading:

Y. Katznelson, An introduction to harmonic analysis, 3rd edition, Cambridge Univ. Press, 2004.
A. Deitmar, A first course in harmonic analysis, Springer, 2002.
E. M. Stein, R. Shakarchi, Fourier analysis: An introduction, Princeton Univ. Press, 2003.
E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970.
E. M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Uinv. Press, 1971.
K. Groechenig, Foundations of time-frequency analysis, Birkhaeuser, 2001.
P. Wojtaszczyk, A mathematical introduction to wavelets, Cambridge Univ. Press, 1997.

The classical book by Katznelson covers the core contents of the course. Deitmar's book is a very elementary and short introduction towards abstract harmonic analysis. The Stein-Shakarchi book is the first in a planned series of three textbooks that might become standard in coming years. Later parts of the course will use pieces from the other books and further sources.

Prerequisites:

Linear Algebra 1 (100221) and Analysis 2 (100212) are prerequisites. It is desirable that students have also attended Integration and Manifolds (110311), talk to the instructor if you haven't taken this course.

Contact Information:

Instructor:	Peter Oswald
Email:	p.oswald@iu-bremen.de
URL:	http://www.faculty.iu-bremen.de/poswald
Phone:	200-3179
Office hours:	Tue 1:30-3pm (or by appointment) in Research I, 113

TA/Grader:	Vladimir Molchanov
Email:	Vladimir
Contact:	Research I, Room 129a, Phone: x3582

Time and Place:

Lectures (subject to change!)

We 8:15-9:30 and Fr 11:15-12:30 in East Hall 3

Homework:

Homework will be handed out roughly once a week. Written solutions need to be turned in on the due date, no late homework will be accepted. Homework is your individual work. You can ask the instructor or the TA for hints. You may also consult books and internet resources, provided you always quote the source. Further details will be announced by the instructor.

Grading:

There will be one Midterm and a Final Exam. The final IUB grade will be computed from the weighted average of percentages of maximal scores with the weights

Homework:	40%
Midterm Exam (week 7):	20%
Final Exam:	40%

according to the following table:

Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67

Last modified: 2006/01/29
This page: http://www.faculty.iu-bremen.de/poswald/Teaching/HarmAnal/HarmAnal.htm
Peter Oswald (p.oswald@iu-bremen.de)