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Functional analysis Semester
WiSe 2021 / 22
Lecturer
Helmut Abels
Type of course (Veranstaltungsart)
Vorlesung
German title
Funktionalanalysis
Contents
Functional analysis is the theory of infinitely dimensional vector spaces and maps between such spaces. Here it is important, which topology we choose. Many classical statements in the field of linear algebra and analysis are not true for infinitely dimensional vector spaces. In this introduction we treat the basic concepts and fundamental principles of the (linear) functional analysis, e.g.
- properties of normed vector spaces and metric spaces,
- examples of important function spaces,
- bounded linear operators and its properties, in particular the principle of uniform boundednessand Theorem of Hahn-Banach,
- dual spaces, adjoint operators, weak convergence and weak compactness,
- spectral theory, in particular for compact operators.
The lecture series will be taught in English if necessary. Otherwise it will be taught in German.
Literature
- H. W. Alt, Lineare Funktionalanalysis, Springer Verlag 2006
- W. Rudin, Functional Analysis, McGraw Hill Higher Education 2007
- D. Werner, Funktionalanalysis, Springer Verlag 2000
- J. Wloka, Funktionalanalysis und ihre Anwendungen, Walter de Gruyter Verlag 1971
- K. Yosida, Functional Analysis, Springer Verlag 2008
Recommended previous knowledge
Analysis I-III, Lineare Algebra I
Time/Date
Mo 12-14 und Thu 8-10
Location
M 103
Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=51152
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)
Registration- Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department) - Registration for the exercise classes: on GRIPS
- Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)- Successful participation in the exercise classes: 50% of the maximal points in the exercise
sheets, satisfactory presentation of one solution.
Examination (Prüfungsleistungen)- Oral exam: Duration: 30 min., Date: by appointment, re-exam: Date:
Modules
BAn(2), BV, MV, MAngAn, CS-B-Math4, CS-M-P1, CS-M-P2, CS-M-P3, PHY-B-WE 03, PHY-M-VE 03
ECTS
9
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