Fourier Analysis (Winter Semester 2014/15)
- Lecturer: Prof. Maria Girardi
- Classes: Lecture (0104550), Problem class (0104560)
- Weekly hours: 4+2
| Announcements |
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The results of the exam are now posted between the rooms 3A-05.1 and 3A-05.2. You may look at your exam on Friday, March 6, from 10:00 to 11:00 am in room 3A-27.
| Schedule | ||
|---|---|---|
| Lecture: | Monday 11:30-13:00 | 1C-03 |
| Monday 11:30-13:00 | SR 2.58 | |
| Wednesday 14:00-15:30 | 1C-01 | |
| Wednesday 14:00-15:30 | SR 2.58 | |
| Problem class: | Tuesday 17:30-19:00 | Z 2 |
| Tuesday 17:30-19:00 | SR 2.58 | |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Maria Girardi | |
| Office hours: by appointment | ||
| Room 2.045 Kollegiengebäude Mathematik (20.30) | ||
| Email: girardi@math.sc.edu | Problem classes | Dr. Martin Spitz |
| Office hours: | ||
| Room Kollegiengebäude Mathematik (20.30) | ||
| Email: | ||
| Prerequisites |
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One should be familiar with basic concepts of Lebesgue Integration Theory (e.g. Hölder's inequality and Lebesgue's Dominated Convergence Theorem) as well as Hilbert and Banach spaces.
| Exercise Sheets |
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Exercise Sheet 1
Exercise Sheet 2
Exercise Sheet 3
Exercise Sheet 4
Exercise Sheet 5
Exercise Sheet 6
Exercise Sheet 7
Exercise Sheet 8
Exercise Sheet 9
Exercise Sheet10
Solution Exercise Sheet 10
References
| References |
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As needed and upon request, references will be added as the semester progresses. Here is a start.
- Folland, Gerald B., Real analysis. Modern techniques and their applications. Second edition. John Wiley & Sons, Inc., New York, 1999. ISBN: 0-471-31716-0.
- Werner, Dirk, Funktionalanalysis. Third edition. Springer-Verlag, Berlin, 2000. ISBN: 3-540-67645-7.
| German/English Assistance |
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We do not want English to be a barrier in this class. If you do not understand the English, just let us know so that we can repeat and/or rephrase. Below are some resources.
| Handouts |
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Reviews of some prequisities
Differentiation under the Integral
Lebesgue's Differentiation Theorem and Lebesgue Sets
Some Basics of Integration on R^N
Multi-index Review
Nets
Nets, cleaner version
Review of Topology
Urysohn's Lemma
Part I: Fourier Series
Tne Circle Group
Properties of the Fourier Coefficients
Table of Fourier Series
Part II: Fourier Transform
Convolution Examples
Fourier Transform Introduction
Families Of Seminorms Generating the Schwartz Class
Riesz-Thorin Interpolation Theorem
Proof of Riesz-Thorin Interpolation Theorem
Distributions Introduction