Universität Wien

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