MAT640
Seminar Introduction to Fourier Analysis
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References for the talks:
[I] Elias M. Stein and Rami Shakarchi, Fourier Analysis: An Introduction, Princeton Lectures in Analysis, Vol. I, Princeton University Press, 2003.
[II] Valery Serov, Fourier Series, Fourier Transform and Their Applications to Mathematical Physics, Applied Mathematical Sciences, Vol. 197, Springer, 2017.
Talks
23.09.2026
1. Basic properties and Fejér’s theorem
[I, Ch. 2]; [II, Chs. 2–5]. (No Abel summability)
[I, Ch. 2]; [II, Chs. 2–5]. (No Abel summability)
Celine Bianca Schälin
30.09.2026
2. Decay of Fourier coefficients and L^2-theory
[I, Sec. 3.1]; [II, Chs. 6–7], in particular Exercises 6.1–6.4. Possibly also [II, Ch. 8].
[I, Sec. 3.1]; [II, Chs. 6–7], in particular Exercises 6.1–6.4. Possibly also [II, Ch. 8].
Alessia Lorena Lopez de Prado Rehder
07.10.2026
3. Pointwise and absolute convergence
[II, Ch. 9 without Petree]; [II, Ch. 10 up to Cor. 10.10]; [I, Sec. 3.2.1].
[II, Ch. 9 without Petree]; [II, Ch. 10 up to Cor. 10.10]; [I, Sec. 3.2.1].
Rahel Astrid Hugener
14.10.2026
4. Further summability results and some (counter-) examples
[I, Sec. 3.2]; [I, Secs. 2.5.3–2.5.4]; [II, Ch. 10 from Cor. 10.11 to the end]; [I, Ch. 4.3].
[I, Sec. 3.2]; [I, Secs. 2.5.3–2.5.4]; [II, Ch. 10 from Cor. 10.11 to the end]; [I, Ch. 4.3].
Moritz Jakob Spengler
21.10.2026
Luca Francesco Luigi Bortoli
18.11.2026
9. Applications: heat equation, Poisson summation formula, and Heisenberg’s uncertainty principle
[I, Chs. 5.1–5.3].
[I, Chs. 5.1–5.3].
Elias Philippe Noschis