SS 2012, Universität Bielefeld

Proseminar Masstheorie und Funktionalanalysis 240034


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)
  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
  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


02.04.2012 - 13.07.2012

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"