Inhalt
[ 201ANLSFANU18 ] UE Functional Analysis
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| (*) Unfortunately this information is not available in english. |
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| Workload |
Education level |
Study areas |
Responsible person |
Hours per week |
Coordinating university |
| 1,5 ECTS |
B2 - Bachelor's programme 2. year |
Mathematics |
N.N. |
1 hpw |
Johannes Kepler University Linz |
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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2025W |
| Learning Outcomes |
Competences |
| A deeper understanding of completeness and compactness in metric and normed spaces is acquired, along with fundamentals related to continuous
operators on Banach and Hilbert spaces.
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| Skills |
Knowledge |
- Investigating compactness in metric spaces and Banach spaces (e.g., the Arzelà-Ascoli theorem)
- Proving continuity of linear mappings (fundamental principles of functional analysis)
- Constructing linear continuous extensions (Hahn-Banach theorem)
- Handling orthonormal systems and projections in Hilbert spaces
- Representing dual spaces (Riesz representation theorem, dual of Lebesgue spaces)
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Completeness and compactness in metric and normed spaces, continuous operators, extensions, orthonormal systems, projections, dual spaces
and the Hahn-Banach theorem.
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| Criteria for evaluation |
“Tick exercise” + Blackboard performance
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| Language |
German |
| Study material |
Every book about elementary functional analysis, e.g. D. Werner – Funktionalanalysis (German)
or J.B. Conway - A Course in Functional Analysis (English).
I can also recommend
G. Folland - Real analysis - modern techniques and their applications
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| Changing subject? |
No |
| Corresponding lecture |
(*)ist gemeinsam mit 201STSTMITU18: UE Maß- und Integrationstheorie (1,5 ECTS) äquivalent zu
TM1PCUEFANA: UE Funktionalanalysis und Integrationstheorie (3 ECTS)
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| On-site course |
| Maximum number of participants |
25 |
| Assignment procedure |
Assignment according to priority |
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