Prof. Dr. Robert Denk

  • Time: Tuesday , 13.30-15.00 in G 309
  • Language: German (English on request)

Content
Literature
Lecture notes
Related Modules
Exam

Content:

Is the space L3(Rn) between the spaces L2(Rn) und L4(Rn)? And if yes, how can we formalize this and obtain new results on the intermediate space? The answer to this is given by the interpolation theory of Banach spaces. This theory allows to interpolate between two Banach spaces, define appropriate intermediate spaces and consider linear operators in this setting.

As applications of interpolation theory, we mention Sobolev spaces and Hölder spaces. We will discuss real and complex interpolation, the theorem of Riesz-Thorin and different scales of non-integer Sobolev spaces.

Prerequisite for this lecture is knowledge of functional analysis. It is also of advantage to have a basic knowledge of semigroup theory and Sobolev space theory.

Literature:

A list of references can be found at the end of the lecture notes.

Lecture notes:

There are lecture notes (in German) which will be updated regularly. The lecture notes can be found in ILIAS.

Related modules:

  • Masterstudiengang Mathematik (88105H)
      6000 Spezialisierungsmodule
        6100 Spezialisierungsmodule
  • Masterstudiengang Mathematik (88105H)
      3000 Wahlmodule
         3100 Wahlmodule 
  • Lehramtsstudiengänge WPO 2001
         (Staatsexamen)
           Mathematik
             Hauptstudium Vorlesungen 
  • Diplomstudiengänge
         Mathematik
             Hauptstudium Vorlesungen

Exam:

To pass this module, one has to participate successfully in the exercise groups and to pass a final oral exam.