The results of the exam are now posted between the rooms 3A-05.1 and 3A-05.2. You may look at your exam on Friday, March 6, from 10:00 to 11:00 am in room 3A-27.
One should be familiar with basic concepts of Lebesgue Integration Theory (e.g. Hölder's inequality and Lebesgue's Dominated Convergence Theorem) as well as Hilbert and Banach spaces.
Exercise Sheet 1
Exercise Sheet 2
Exercise Sheet 3
Exercise Sheet 4
Exercise Sheet 5
Exercise Sheet 6
Exercise Sheet 7
Exercise Sheet 8
Exercise Sheet 9
Solution Exercise Sheet 10
As needed and upon request, references will be added as the semester progresses. Here is a start.
- Folland, Gerald B., Real analysis. Modern techniques and their applications. Second edition. John Wiley & Sons, Inc., New York, 1999. ISBN: 0-471-31716-0.
- Werner, Dirk, Funktionalanalysis. Third edition. Springer-Verlag, Berlin, 2000. ISBN: 3-540-67645-7.
We do not want English to be a barrier in this class. If you do not understand the English, just let us know so that we can repeat and/or rephrase. Below are some resources.
- Prof. Girardi's mathematical German-English cheat sheet: pdf and ods.
Reviews of some prequisities
Differentiation under the Integral
Lebesgue's Differentiation Theorem and Lebesgue Sets
Some Basics of Integration on R^N
Nets, cleaner version
Review of Topology
Part I: Fourier Series
Tne Circle Group
Properties of the Fourier Coefficients
Table of Fourier Series
Part II: Fourier Transform
Fourier Transform Introduction
Families Of Seminorms Generating the Schwartz Class
Riesz-Thorin Interpolation Theorem
Proof of Riesz-Thorin Interpolation Theorem