101.718 Theory of Distributions
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2018S, VO, 2.0h, 3.0EC

Properties

  • Semester hours: 2.0
  • Credits: 3.0
  • Type: VO Lecture

Aim of course

The theory of distributions is a generalization of classical analysis, which makes it possible to systematically deal with difficulties that have been overcome beforehand by ad hoc constructions, or by heuristic arguments. The theory was created by Laurent Schwartz in the 20th century and gives a unified broader framework in which one can reformulate and develop classical problems in engineering, physics, and mathematics.   Distributions have many very different properties. They are a generalization of the notion of function, and their purpose is to solve problems of differentiation. Indeed, every distribution is differentiable and even infinitely differentiable, and the derivatives are also distributions. If a continuous function is not differentiable, then, considered as a distribution, it always admits a derivative, but the derivative is a distribution which is not necessarily a function. This is why distributions are widely used in the analysis of partial differential equations.   The aim of the course is to make the interested student acquainted with the foundations of the theory of distributions as introduced by Schwartz in the elegant framework of topological vector spaces. Applications in partial differential equations and harmonic analysis will be emphasized whenever possible. Last but not least, the theory of distributions is a beautiful piece of mathematics, and the course is surely a good opportunity for all those persons who are interested in broadening their foundational mathematical baggage.  

Subject of course

Topological vector spaces. Locally Convex Spaces. Fréchet spaces. Fundamental function spaces. Space of distributions. Tensor product of Distributions. Convolutions of Distributions.  

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Tue12:00 - 13:0006.03.2018Sem.R. DA grün 03 C First meeting to fix the lecture schedule / dates
Fri13:30 - 15:0009.03.2018 - 29.06.2018Sem.R. DA grün 03 C Theory of distributions
Theory of Distributions - Single appointments
DayDateTimeLocationDescription
Tue06.03.201812:00 - 13:00Sem.R. DA grün 03 C First meeting to fix the lecture schedule / dates
Fri09.03.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri16.03.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri23.03.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri13.04.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri20.04.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri27.04.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri04.05.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri18.05.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri25.05.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri01.06.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri08.06.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri15.06.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri22.06.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions
Fri29.06.201813:30 - 15:00Sem.R. DA grün 03 C Theory of distributions

Examination modalities

oral exam

Course registration

Not necessary

Curricula

Literature

No lecture notes are available.

Previous knowledge

  • the lecture will built on the prerequisites of Analysis 3 (Lebesgue integration theory)
  • knowledge of basic functional analysis and Sobolev spaces is of advantage

Language

English