19219801 Theory of function spaces and applications
Winter Term 2021/2022
lecture and exercise by Dr. Willem van Zuijlen
Time and place
Lecture: Tuesdays 14:00-16:00h.
During the first meeting we will discuss in which form the lecture will take place.
- Final Exam: to be announced in due course
Prerequisits: Analysis I — III, Linear Algebra I, II, Functional Analysis.
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.
- Testfunctions and distributions;
- Convolutions and mollifiers;
- Fundamental solutions of PDEs;
- Sobolev spaces;
- Schwarz functions and tempered distributions;
- Fourier transform and Fourier multipliers;
- Besov spaces;
- Bony para- and resonance products.
During the course lecture notes will be provided, they will be an update from the ones used at the SoSe2020 which can be found on the website of the teacher: https://www.wias-berlin.de/people/vanzuijlen/LN_theory_of_function_spaces.pdf