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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.

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 MyCampus/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.

  • 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.

References

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