Vorlesung: Fourier Series (WiSe 2025-26)
Lecture (Vorlesung):
Tue 12-14 & Thu 12-14 (both in B 005). LSF
Exercises (Übungen):
See separate webpage (Moodle). LSF
Tutorials (Tutorien):
See separate webpage (Moodle).
Synopsis (Kurzbeschreibung):
(More details on content below.)
NB Die Vorlesung wird auf Englisch gehalten.
Audience (Hörerkreis):
Students pursuing the following degrees: BSc Mathematics, BSc Financial Mathematics.
Credits:
9 (6+3) ECTS.
Prerequisites (Vorkenntnisse):
Analysis I-III, Lineare Algebra I-II. You find handouts with the needed facts (without proofs, and to be updated!) below, and in Moodle.
Language (Sprache):
English.
Exam (Prüfung):
See Moodle.
Content (Inhalt):
- Recapitulation of basic notions PDF (Handout: Topological and metric spaces (Ana2))
0.1 Topological spaces
0.2 Metric spaces - Bounded operators
5.1 Topologies on the space of bounded linear operators PDF
In Moodle you will find a copy of the notes from the lecture (to be updated as we go along).
Above you will find a short description of the content of the lecture.
The course will not follow a particular textbook. The list below provides a short selection of English and German textbooks on the subject (of which there are many!).
Supplementary literatur (Ergänzende Literatur):
- A. Deitmar, A First Course in Harmonic Analysis, Springer, 2005.
- G. B. Folland, Fourier analysis and its application, AMS, 1992.
- J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981.
- W. Kaballo, Grundkurs Funktionalanalysis, 2. Auflage, Springer Spektrum, 2018.
- W. Kaballo, Aufbaukurs Funktionalanalysis und Operatortheorie, Springer Spektrum, 2014.
- Y. Katznelson, An introduction to Harmonic Analysis, 3rd edition, CUP, 2004.
- M. A. Pinsky, Introduction to Fourier Analysis and Wavelets, AMS, 2009.
Office hours (Sprechstunde):
See Moodle.
To access the course material, you need to sign up (opens ??. October 2025) in Moodle here (Psword: Carleson) .
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Letzte Änderung: 10 July 2025.
Thomas Østergaard Sørensen