240034 Maßtheorie und Funktionalanalysis (PS) (SoSe 2012)

REMARK: This moment there are no participants in this
seminar and no talk is scheduled to take place,
but you can still participate in this seminar if you wish.
If this is the case, please contact me as soon as possible.
(It is also possible to write your ``Bachelorarbeit"
based on the contents of the talk.)

List of suggested topics:

1. Stone-Weierstrass theorem and its applications
2. Baire's category theorem and its applications
3. L^p-spaces and their duals
4. Weak topologies on Banach spaces and applications
5. Fixed point theorems and their applications
6. Pointwise convergence and non-convergence of Fourier series
7. Hausdorff measure and Hausdorff dimension with applications to fractal geometry
8. Linear functionals on continuous functions and Riesz(-Markov-Kakutani) representation theorem
Advanced related topic: Daniell-Stone integrals and their applications
9. Absolutely continuous functions and Lebesgue's differentiation theorem
10. Fourier transform and its applications to differential equations
11. Sobolev spaces and Sobolev embedding theorem
12. Harmonic functions and the Dirichlet problem for Laplace's equation
13. Optimal transport problem

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Good knowledge of measure theory and integration theory is assumed. Knowledge of basic functional analysis
will be helpful, but you can learn it later during the preparation for your seminar talk.

Externe Kommentarseite

http://www.math.uni-bielefeld.de/~nkajino/lectures/MassFunkt2012.html