Inhalt
[ 201ANLSFANV18 ] VL Functional Analysis
|
|
|
|
| (*) Unfortunately this information is not available in english. |
 |
| Workload |
Education level |
Study areas |
Responsible person |
Hours per week |
Coordinating university |
| 4,5 ECTS |
B2 - Bachelor's programme 2. year |
Mathematics |
N.N. |
3 hpw |
Johannes Kepler University Linz |
|
|
|
| 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.
|
|
| 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)
|
Completeness and compactness in metric and normed spaces, continuous operators, extensions, orthonormal systems, projections, dual spaces
and the Hahn-Banach theorem.
|
|
| Criteria for evaluation |
Written exam at the end of the semester
|
| Methods |
Blackboard talk combined with lecture notes
|
| 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
|
| Changing subject? |
No |
| Corresponding lecture |
(*)ist gemeinsam mit 201STSTMITV18: VL Maß- und Integrationstheorie (3 ECTS) äquivalent zu
TM1PCVOFANA: VO Funktionalanalysis und Integrationstheorie (6 ECTS) +
[ Lehrveranstaltung aus dem Wahlfach a. Analysis (1,5 ECTS) oder
Lehrveranstaltung aus dem Wahlfach k. Funktionalanalysis (1,5 ECTS) ]
|
|
|
|
| On-site course |
| Maximum number of participants |
- |
| Assignment procedure |
Direct assignment |
|
|
|
