Admission requirements
Knowledge of linear algebra, elementary topology, real analysis, Lebesgue integration.
It is highly recommended that the students have followed the course on Linear Analysis.
Knowledge of complex analysis is a plus but not a must.
Description
The course focuses on the theory and applications of Fourier series and the Fourier transform.
Starting from Lebesgue integration and Hilbert spaces, in the first part of the course we will introduce classical Fourier theory, focusing on the Fourier series and the Fourier transform on the real line.
The second part of the course will focus on the Fourier transform on (tempered) distributions. If time allows, we will study applications to the representation theory of Abelian groups.
Course objectives
The student knows and understands the treated course material and is able to reproduce the content of the course. The student is able to apply the methods of Fourier analysis to concrete problems as well as to problems from different areas of mathematics.
Mode of instruction
Lectures: 2 hours per week.
During the course, individual students can hand in a number of assignments, according to a schedule that is provided in Blackboard at the start of the semester.
Assessment method
During the course, individual students can hand in a number of assignments, according to a schedule that is provided in Blackboard at the start of the semester. The lowest grade for these is stricken, and the homework grade is determined as the (unrounded) average of the remaining grades for these assignments.
The unrounded final grade for the course is the maximum of:
the weighted average of the homework grade (25%),
the maximum of the (unrounded) grades for the written exam and the resit (75%),
the (unrounded) grade for the written exam, and
the (unrounded) grade for the resit.
This maximum is then rounded to the nearest half-integer, but not to 5.5, to obtain the final grade for the course. If the result is 6.0 or higher, this is a "pass", provided that a grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit. If the result is 5.0 or lower, or if no grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit, this is a "fail".
During the written exam and the resit you can use the textbook of the course and the notes that you may have taken.
Literature
Strichartz, Robert S. A guide to distribution theory and Fourier transforms. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. x+226 pp. ISBN: 981-238-430-8 MR2000535
Körner, T. W. Fourier analysis. Cambridge University Press, Cambridge, 1988. {\rm xii}+591 pp. ISBN: 0-521-25120-6 MR0924154
Brightspace/website
Brightspace.