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401-3461-00L 9 Credits BSC , MSC D-MATH , D-PHYS
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Functional Analysis I

Lecturers & Examiners: Prof. Dr. Tristan Rivière
At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office ( ) after having received the credits.
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Last Updated: 2026-06-01 11:31:15

Abstract

Banach and Hilbert spaces, bounded linear operators; Hahn Banach, Baire Category, Uniform boundedness and Banach Steinhaus Theorem, open mapping/closed graph theorem; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; Uniformly Convex Spaces; Application to L^p Spaces; Compact operators, Spectral theory of self-adjoint compact operators. Sobolev spaces.

Objective

Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis for future aplications to the Analysis of Partial Differential Equations, Harmonic Analysis, Function Spaces Theory, Operator Theory, Probability Theory, Stochastic Analysis, Numerical Analysis.

Resources

Literature

Recommended references include the following: Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011. Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
One handwritten DIN A4 sheet (2-sided).

Course Components

Type Title Time & Place Hours
lecture Functional Analysis I
  • Mon 10:15-12:00 (HG D 1.1)
  • Thu 14:15-16:00 (HG G 5)
4 h weekly
exercise Functional Analysis I
Groups are selected in myStudies.
  • Mon 09:15-10:00 (HG G 26.1)
  • Mon 09:15-10:00 (HG G 26.5)
  • Mon 09:15-10:00 (ML F 40)
  • Mon 09:15-10:00 (ML J 34.1)
1 h weekly

Offered In