Fourier Analysis (MATS315) Fourier-analyysi
General Information
- Begins ~ ends: September 1, 2022 ~ October 20, 2022
- Instructor: Pu-Zhao Kow
- Email: pu-zhao.pz.kow [at] jyu.fi
- Office: MaD369, Department of Mathematics and Statistics, Mattilanniemi building D (MaD)
- Teaching Language: English
- Lecture Note: Pu-Zhao Kow, Fourier analysis and distribution theory. Note: The lecture note may update during the course.
- Following up course: Fourier Analysis II (MATS5170), lectured by Tuomas Orponen. The course will be lectured in English.
References
- F. G. Friedlander and M. Joshi, Introduction to the theory of distributions, Second edition. Cambridge University Press, Camgridge, 1998. MR1721032
- Dorina Mitrea, Distributions, partial differential equations, and harmonic analysis, Second edition. Universitext. Springer, Cham, 2018. MR3887685, doi:10.1007/978-3-030-03296-8.
- Mikko Salo, Fourier analysis and distribution theory, Lecture notes, Fall 2013.
Prerequisite
- Multivariable calculus
Homeworks
- Homework 1, return by September 16, 2022 (Friday)
- Homework 2, return by September 23, 2022 (Friday)
- Homework 3, return by September 30, 2022 (Friday)
- Homework 4, return by October 07, 2022 (Friday)
- Homework 5, return by October 14, 2022 (Friday)
Schedule
- The lectures are on Thursday and Friday at 10.15 - 12.00 in MaD380 (Thursday) and MaD381 (Friday). Exercise sessions are on Thursday at 08.30 - 10.00 in MaD355.
| Time | Room | Activities |
|---|---|---|
| 01.09.2022 10.15-12.00 | MaD380 | Week 1 - Lecture (Thursday): weak derivative and Fourier series in L2 |
| 02.09.2022 10.15-12.00 | MaD381 | Week 1 - Lecture (Friday): Fourier series in L2 |
| 08.09.2022 08.30-10.00 | MaD355 | Week 1 - Exercise Session |
| 08.09.2022 10.15-12.00 | MaD380 | Week 2 - Lecture (Thursday): Convergence of Fourier series, Schwartz functions |
| 09.09.2022 10.15-12.00 | MaD381 | Week 2 - Lecture (Friday): Schwartz functions |
| 15.09.2022 08.30-10.00 | MaD355 | Week 2 - Exercise Session |
| 15.09.2022 10.15-12.00 | MaD380 | Week 3 - Lecture (Thursday): Tempered distributions |
| 16.09.2022 10.15-12.00 | MaD381 | Week 3 - Lecture (Friday): Tempered distributions and distributions with compact support [Return Homework 1] |
| 22.09.2022 08.30-10.00 | MaD355 | Week 3 - Exercise Session |
| 22.09.2022 10.15-12.00 | MaD380 | Week 4 - Lecture (Thursday): Distributions and convolution |
| 23.09.2022 10.15-12.00 | MaD381 | Week 4 - Lecture (Friday): Convolution [Return Homework 2] |
| 29.09.2022 08.30-10.00 | MaD355 | Week 4 - Exercise Session |
| 29.09.2022 10.15-12.00 | MaD380 | Week 5 - Lecture (Thursday): Structure of distributions and convolution theorem |
| 30.09.2022 10.15-12.00 | MaD381 | Week 5 - Lecture (Friday): Structure of distributions and convolution theorem [Return Homework 3] |
| 06.10.2022 08.30-10.00 | MaD355 | Week 5 - Exercise Session |
| 06.10.2022 10.15-12.00 | MaD380 | Week 6 - Lecture (Thursday): Convolution theorem and pv distributions |
| 07.10.2022 10.15-12.00 | MaD381 | Week 6 - Lecture (Friday): pv distributions [Return Homework 4 and final report] |
| 13.10.2022 08.30-10.00 | MaD355 | Week 6 - Exercise Session |
| 13.10.2022 10.15-12.00 | MaD380 | Week 7 - Lecture (Thursday): Final presentation |
| 14.10.2022 10.15-12.00 | MaD381 | Week 7 - Lecture (Friday): Final presentation [Return Homework 5] |
| 20.10.2022 08.30-10.00 | MaD355 | Week 7 - Exercise Session |
Completion
- The course can be taken for credit by attending the lectures, returning written solutions (at least 50%, please indicate your email) and writing a short report (not more than 10 pages) with an oral presentation on it at the end of the course. One possible topic for the final report is some theorems in the lecture note that the proofs are omitted. To get grade 5, you need to complete at least 80% of the returning written solutions.
- If you wish to give oral presentation earlier (e.g. Week 6), please let me know as soon as possible. Please remember send me your final report before oral presentation.