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| Semester | spring semester 2023 |
| Course frequency | Irregular |
| Lecturers | Gaspard Ohlmann (gaspard.ohlmann@unibas.ch, Assessor) |
| Content | In this course, we provide an introduction to Fourier Analysis. First, we study periodic functions and Fourier series. Later on, we introduce several tools commonly used in analysis and use them to study the Fourier transform and its properties. Chapter I: Fourier Series I.1 : Trigonometric polynomials, L^2 scalar product and orthogonality I.2 : Fourier series, definition and properties I.3 : Bessel’s inequality I.4 : Unicity of the Fourier series for continuous functions I.5 : Results on convergence I.6 : Relationship between the decay of the coefficients and the regularity of the function. Chapter II: Analysis preliminaries II.1 The Schwarz space II.2 Convolution of functions II.3 Approximations of the identity: definition and properties II.4 Density of the Schwarz space in L^p II.5 Density of L^p in L^q Chapter III: The Fourier transform III.1 : Definition of the Fourier transform on L^1 III.2 : Properties of the Fourier transform: derivative, convolution, translation III.3 : Plancherel theorem III.4 : The inverse Fourier transform III.5 : Extension of the Fourier transform to L^2 and properties. III.6 : Applications It is recommended to have done "mass und integrationtheorie" for this lecture, but not mandatory. |
| Learning objectives | At the end of the lecture, you should have seen all the basic properties of the Fourier analysis and have a good understanding of it. Also, advanced topics in analysis are introduced in this lecture and should be helpful for any later analysis course. |
| Language of instruction | English |
| Use of digital media | No specific media used |
| Course auditors welcome |
| Interval | Weekday | Time | Room |
|---|---|---|---|
| wöchentlich | Thursday | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Date | Time | Room |
|---|---|---|
| Thursday 23.02.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 02.03.2023 | 14.15-16.00 | Fasnachstferien |
| Thursday 09.03.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 16.03.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 23.03.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 30.03.2023 | 14.15-16.00 | Alte Universität, Besprechung 003 |
| Thursday 06.04.2023 | 14.15-16.00 | Ostern |
| Thursday 13.04.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 20.04.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 27.04.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 04.05.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 11.05.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 18.05.2023 | 14.15-16.00 | Auffahrt |
| Thursday 25.05.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Thursday 01.06.2023 | 14.15-16.00 | Spiegelgasse 1, Seminarraum 00.003 |
| Modules |
Module: Analysis and Geometry (Bachelor's Studies: Mathematics) |
| Assessment format | continuous assessment |
| Assessment registration/deregistration | Reg.: course registration, dereg: cancel course registration |
| Repeat examination | no repeat examination |
| Scale | Pass / Fail |
| Repeated registration | as often as necessary |
| Responsible faculty | Faculty of Science, studiendekanat-philnat@unibas.ch |
| Offered by | Fachbereich Mathematik |