After successful completion of the course, students are able to...

• Understand the role of the theory of distributions in other areas of modern analysis, especially in Partial Differential Equations;
• Specify properties of fundamental function spaces and of the space of distributions and derive statements from them; 
• Explain Radon measures, Sobolev, and BV functions as examples of distributions of finite-order, and to derive statements about them;
• Apply the ideas and methods of the Theory of Distributions to prove central theorems of modern analysis.

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

Online-Lecture for presenting the material and discussions.

Scheduling and first lecture: Tuesday, 5. 10., 11:15-12:45 on Zoom. In case of time conflict contact the lecturer.

Zoom-Link: https://tuwien.zoom.us/j/94586426525?pwd=N2pxTUludm5HLzd0bDE2SDdFa3hUQT09

Oral exam.

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