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 Calculus of Variations and Partial Differential Equations;
• Manage abstract results in the context of topological vector spaces, locally convex spaces and Fréchet spaces;
• 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.  

Lecture. 2 hours per week. The instructor will spend most of the class time on presenting the new material. The students are encouraged to ask questions and seek help from the instructor, both in and out of class.

The examination consists of an oral exam or a written project. During the course, there may be optional assignments that give bonus points on the 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