Fall 2017
The course will include (some or all of) the following areas, but may well be expanded, depending on participants and examiner.
Functional Analysis, Geometric Measure Theory, Ergodic Theory, Probabilistic Techniques, Harmonic Analysis on Groups, Sobolev Spaces.
After completing the course:
Students should have general knowledge of several classical topics in Analysis and their applications in other areas of mathematics.
Students are supposed to have in-depth knowledge of at least one area outside their own research, and its connection to other areas.
Students should be familiar with technical tools from the areas represented at the course.
Students should have a heuristic overview of the topics given at the course.
Attendance are required to have god knowledge in Analysis and Algebra at master level, and some basic probability theory.
Robert Zimmer: Functional analysis
Pertti Mattila: Geometry of sets and measures in Euclidean spaces.
Peter Walters: An introduction to Ergodic theory
Richard F. Bass: Probabilistic Techniques in Analysis
Katznelson: An introduction to Harmonic Analysis.
Folland: A course in abstract harmonic analysis
Bressan: Lecture Notes on Sobolev Spaces
R. Adams, J.F. Fournier: Sobolev Spaces
If the course is discontinued, students may request to be examined during the following two academic years.
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Examination will consist of one topic presentation by students, as well as homework.
Approved homework assignments, and oral presentation of a project with written report.
