19219801 Theory of function spaces and applications
Summer Term 2020
lecture and exercise by Dr. Willem van Zuijlen
Time and place
Lecture: Video lectures will be available online (details TBA).
Online "office hours": Tuesdays 10:00-12:00h.
- Final Exam: to be announced in due course
Prerequisits: Analysis I — III, Linear Algebra I, II, Functional Analysis.
If you are an FU student you only need to register for the course via CM (Campus Management).
If you are not an FU student, you are required to register via KVV/Whiteboard.
Exercises: Every week a new part of lecture notes will come available with excersises.
Course Overview/ Content:
In this course we consider function spaces and more general spaces of distributions, which are generalized functions. The main key in the course is the theory of Harmonic Analysis, which is used to define Besov spaces. Moreover, we treat Bony's para- and resonance products, which allow us to multiply distributions in some cases.
- Introducing generalisation of functions: distributions;
- Topologies on spaces of distributions;
- Fourier transform (of distributions);
- Fourier multipliers;
- Sobolev and Besov spaces;
- Bony para- and resonance products.
There will be lecture notes.