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Functional Analysis I
Last Updated: 2026-06-03 00:07:49
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.
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 | No time listed | 4 h weekly |
| exercise | Functional Analysis I | No time listed | 1 h weekly |
Offered In
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Bachelor Core Courses: Pure Mathematics (Further restrictions apply, but in particular: 401-3531-00L Differential Geometry I can only be recognised for the Master Programme if 401-3532-00L Differential Geometry II has not been recognised for the Bachelor Programme. Analogously for: 401-3461-00L Functional Analysis I - 401-3462-00L Functional Analysis II 401-3001-61L Algebraic Topology I - 401-3002-12L Algebraic Topology II 401-3132-00L Commutative Algebra - 401-3146-12L Algebraic Geometry For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
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