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Functional Analysis with Applications

This is the study programme for 2019/2020. It is subject to change.

The course is designed both for PhD graduates in mathematical analysis and for PhD candidates in probability theory and stochastic processes. The course presents some selected topics in functional analysis such as is an important basis for understanding the ideas of probability theory and stochastic processes.

Learning outcome

After completing the course the student will have knowledge of key concepts and ideas in functional analysis and their applications, especially in probability theory. Students can work with tools from measure theory and Lebesgueintegrasjon, determine questions about different types of convergence, and apply it to some kinds of stochastic processes.


Measure theory, integration theory. Topological and standardized space, Hilbert space. Distributions. Stochastic processes.

Required prerequisite knowledge


Recommended previous knowledge

General mathematics knowledge at masters level.


Weight Duration Marks Aid
Oral exam1/14 hoursPass - FailNone permitted

Course teacher(s)

Course coordinator
Alexander Ulanovskii
Course teacher
Alexander Rashkovskii , Jan Terje Kvaløy
Head of Department
Bjørn Henrik Auestad

Method of work

5-6 hours of lectures and exercises per week. If few students sign up the course may be arranged as self study.

Open to

Technology and Natural Science - PhD programme

Course assessment

Usually by forms and/or discussion according to university regulations.


`Linear Functional Analysis' by J. Cerda; `Functional Analysis for Probability and Stochastic Processes. An Introduction' by A. Bobrowski. Accurate syllabus given at semester start.

This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 05.06.2020