Departments' graduate courses
Course start and periodicity may vary. Please see details for each course for up-to-date information. The courses are managed and administered by the respective departments. For more information about the courses, how to sign up, and other practical issues, please contact the examiner or course contact to be found in the course information.
- Course code: FMVE025
- Course higher education credits: 7.5
- Department: MATHEMATICAL SCIENCES
- Graduate school: Mathematics
- Course start: 2015-11-02
- Course end: 2015-12-18
- Course is normally given: Period 2, every year
- Language: The course will be given in English
The basic idea of functional analysis is to apply geometric methods to functions and function spaces. A function is considered as a point in a space, and this space will be a vector space of infinite dimension. Geometric objects like balls, and also convergence, are introduced in these spaces.
For more information, see the course homepage:
G. Folland: Real Analysis. Modern Techniques and their Applications, John Wiley & Sons, 1999,Chapters 5-7 and parts of Chapter 4.
Content of course
(The numbers refer to chapters and section in Folland's book).
5.1 normed linear spaces
6.1,2 Lp spaces and their duals
5.2 the Hahn-Banach theorem
5.3 Baire's theorem with consequences
5.5 Hilbert spaces
from 5.4 the separable case of Alaoglu's theorem
from Chap. 4 Urysohn's lemma in locally compact Hausdorff spaces
7.1,2 the Riesz representation theorem, positive case
7.3 idem, signed case
6.3,4,5 more on Lp spaces, interpolation
5.4 topological vector spaces, weak topologies, the general case of Alaoglu's theorem (if there is time)
Lyudmila Turowska, firstname.lastname@example.org