## SS 2012, Universität Bielefeld

## Proseminar Masstheorie und Funktionalanalysis 240034

### Topics

Each student in this seminar is supposed to choose one topic
from the list of topics given below and to give a

talk of 90 minutes on the chosen topic. The topics are
adopted from measure theory and/or functional analysis.

#### List of suggested topics

Pdf version (with references)
- Stone-Weierstrass theorem and its applications
- Baire's category theorem and its applications
- L^p-spaces and their duals
- Weak topologies on Banach spaces and applications
- Fixed point theorems and their applications
- Pointwise convergence and non-convergence of Fourier series
- Hausdorff measure and Hausdorff dimension with applications to fractal geometry
- Linear functionals on continuous functions and Riesz(-Markov-Kakutani) representation theorem
- Advanced related topic: Daniell-Stone integrals and their applications

- Absolutely continuous functions and Lebesgue's differentiation theorem
- Fourier transform and its applications to differential equations
- Sobolev spaces and Sobolev embedding theorem
- Harmonic functions and the Dirichlet problem for Laplace's equation
- Optimal transport problem

### Talks

02.04.2012 - 13.07.2012
- (Mondays 14:15-15:45 in C01-249)

There were no participants in this seminar and no talk was scheduled.

Naotaka Kajino

Department of Mathematics,
Graduate School of Science,
Kobe University,

Rokkodai-cho 1-1, Nada-ku, 657-8501 Kobe, Japan

Office: Faculty of Science Building B, Room B426

Tel: +81-78-803-5616

Fax: +81-78-803-5610

E-mail: nkajino ``at" math.kobe-u.ac.jp