Institutionernas doktorandkurser

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Functional analysis

  • Kurskod: FMVE025
  • ECTS-poäng: 7,5
  • Forskarskola: Matematik
  • Startdatum: 2015-11-02
  • Slutdatum: 2015-12-18
  • Periodicitet: Läsperiod 2, varje år
  • Undervisningsspråk: Kursen kommer att ges på engelska
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
Mer information
Lyudmila Turowska,

Sidansvarig Publicerad: on 10 feb 2021.