MA8106 Harmonic Analysis Spring 2020
- I am going to try to provide notes for the material covered in the upcoming lectures and I suggest to use the Thursday lectures to go through the material. The plan is to use the program zoom for the online supervision on Thursday at 10:15. See zoom for instructions on installing zoom, etc.
- This week we are going to finish the proof of Theorem 3.5.15, volume 1, B. Simon. Discussion of the Theorem of Stone-Weierstrass following the notes Stone-Weierstrass.
- Within the next days I am going to post an outline for the remaining lectures, see Lectures log.
We are going to treat the Hilbert transform, convergence of Fourier series in different settings (uniform, pointwise, a.e., in Lebesgues spaces), real and complex interpolation, Hardy-Littlewood maximal functions, singular integral operators, as a preparation we review the key definitions, constructions and theorems of the theory of L^p-spaces and Lorentz spaces.
Furthermore, we are discussing the extension of Fourier series to locally compactgroups, including the construction of the Haar measure on a locally compact groups and Pontragjin duality for locally compact abelian groups, etc.
- Part of the material is going to be from Barry Simon's "A Comprehensive Course in Analysis", AMS, 2015, in particular Part 3 on "Harmonic Analysis".
- There is also a number of lecture notes on the web that I am going to take material from, e.g. Terry Tao's Lecture Notes on Harmonic Analysis Lecture notes etc.
- I'll announce the sources before the lectures take place.
* Mondays 10:15-12:00: Simastuen, room 656 * Thursdays 10:15-12:00: Seminarrom 822
Lecturer: Franz Luef