# MA8106 Harmonic Analysis Spring 2020

Messages:

• 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.

## Content

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.

## Teaching material

• 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.

## Lectures

* Mondays 10:15-12:00: Simastuen, room 656
* Thursdays 10:15-12:00: Seminarrom 822 

Lecturer: Franz Luef