Universität Wien
Warning! The directory is not yet complete and will be amended until the beginning of the term.

250113 VO Colombeau Algebras (Sel. topics mod. Analysis) (2005W)

Selected topics in modern Analysis: Colombeau Algebras

0.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 04.10. 13:20 - 14:30 Seminarraum
  • Wednesday 05.10. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 11.10. 13:20 - 14:30 Seminarraum
  • Wednesday 12.10. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 18.10. 13:20 - 14:30 Seminarraum
  • Wednesday 19.10. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 25.10. 13:20 - 14:30 Seminarraum
  • Tuesday 08.11. 13:20 - 14:30 Seminarraum
  • Wednesday 09.11. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 15.11. 13:20 - 14:30 Seminarraum
  • Wednesday 16.11. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 22.11. 13:20 - 14:30 Seminarraum
  • Wednesday 23.11. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 29.11. 13:20 - 14:30 Seminarraum
  • Wednesday 30.11. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 06.12. 13:20 - 14:30 Seminarraum
  • Wednesday 07.12. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 13.12. 13:20 - 14:30 Seminarraum
  • Wednesday 14.12. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 10.01. 13:20 - 14:30 Seminarraum
  • Wednesday 11.01. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 17.01. 13:20 - 14:30 Seminarraum
  • Wednesday 18.01. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 24.01. 13:20 - 14:30 Seminarraum
  • Wednesday 25.01. 13:00 - 14:05 Büro Dipl./Diss.
  • Tuesday 31.01. 13:20 - 14:30 Seminarraum

Information

Aims, contents and method of the course

This lecture offers an introduction into the at present highly active field of
nonlinear theories of generalized functions. As a follow-up to this lecture,
composition of a diploma resp. doctoral thesis in this branch of mathematics
should be possible, with one of the members of the group DIANA supervising
(DIANA: DIfferential Algebras and Nonlinear Analysis; M. Grosser, G. Hörmann,
M. Kunzinger, R. Steinbauer, Wien; [M. Oberguggenberger, Innsbruck; James
Vickers, Southampton, Claudia Garetto, Innsbruck at present]).

The lecture starts with a brief review of the theory of distributions. The
first part then gives an introduction into the basic questions of
multiplication of distributions by studying numerous examples; the need for a
"nonlinear'' theory is highlighted. In parts two and three, respectively, the
"special" and the "full" variants of Colombeau algebras are presented, each
of which contains the distributions as a linear subspace. The concluding
section offers an outlook at diffeomorphism-invariant Colombeau algebras and
at those defined on differentiable manifolds.

Prerequisites: Knowledge of the material covered by the introductory lectures
of the first part of the diploma curriculum (analysis; linear algebra) and of
the topology of metric spaces; proficiency in the fields of functional
analysis and the theory of measure and integration might be useful now and
then, yet is not strictly required.

Examinations: oral, according to individual arrangement.

Assessment and permitted materials

Minimum requirements and assessment criteria

the obvious ones

Examination topics

as to content: all mathematical techniques
as to organizing the process of teaching and learning: see

http://www.mat.univie.ac.at/studentinfo/studienplan/Studienplan-Diplom3.html

Reading list

FRIEDLANDER, Gerard, JOSHI, Mark: Introduction to the theory of distributions,
Cambridge 1998.

OBERGUGGENBERGER, Michael: Multiplication of distributions and applications to
partial differential equations, Longman, Harlow 1992.

GROSSER, Michael, KUNZINGER, Michael, OBERGUGGENBERGER, Michael, STEINBAUER,
Roland: Geometric Theory of Generalized Functions with Applications to
General Relativity, Kluwer, Dordrecht 2001.

Association in the course directory

Last modified: Mo 07.09.2020 15:40