Winter semester 2020/2021
Functional analysis I
General Information
News
Lecturer
Assistant
Creditpoints
9 ECTS
First lecture
03.11.2020
Weekly lectures
Tue 10.00 a.m - 12.00 p.m., Thu 12.00 p.m. - 14.00 p.m.
Content
The course gives an introduction to the basic principles of funtional analysis in normed linear spaces. Among the topics treated are:
Metric spaces, Banach spaces, Hilbert spaces, the theorem of Hahn-Banach, the open mapping theorem,
the closed graph theorem, the uniform boundedness principle, duality and reflexivity, and the spectral theory for operators on Banach and Hilbert spaces.
Prerequisites
Analysis I+II, Linear Algebra I+II, prior knowledge of complex analysis is helpful, but not required
Exams
Admission requirements and type of the exam
To be admitted to the exam, you need 50 % of the points achievable in the homework assignments.
Depending on the number of participants there will be a written or an oral exam.
Examination dates
The way things are at the moment there will be written exams at:
- Tuesday, 16.02.2021, 9 a.m. - 12 p.m, lecture hall I+II+III in E 2.5
- Tuesday, 30.03.2021, 9 a.m. - 12 p.m., lecture hall I in E 2.5
Registration for the exam
Until one week before the corresponding exam via LSF/HISPOS. In case of problems please contact
Prof. Dr. Jörg Eschmeier or Sebastian Toth.
Exercises
Tutorial groups
There will be a weekly tutorial in form of a video conference. In the tutorials solutions of the homework problems will be presented.
Material
Lecture notes
FA_1_Section_1FA_1_Section_2FA_1_Section_3FA_1_Section_4_(a)FA_1_Section_4_(b)FA_1_Section_5_(a)FA_1_Section_5_(b)FA_1_Section_6_(a)FA_1_Section_6_(b)FA_1_Section_7_(a)FA_1_Section_7_(b)FA_1_Section_7_(c)FA_1_Section_8FA_1_Section_9FA_1_Section_10FA_1_Section_11_(a)FA_1_Section_11_(b)FA_1_Section_12_13FA_1_Section_14_(a)FA_1_Section_14_(b)FA_1_Useful_facts
Skript
(Unfortunately the Lecture notes written with Latex are only available in German.)
Skript
(Unfortunately the Lecture notes written with Latex are only available in German.)
Exercise sheets
Every week there will be a new exercise sheet. You may submit the solutions for the exercise sheets in groups up to three participants, belonging to the same tutorial group.
Because of the corona pandemic please do not meet in person. Solutions of the homework problems have to be submitted via CMS one week after the exercise sheet has been uploaded on the homepage.
Sheet 1Sheet 2Sheet 3Sheet 4Sheet 5Sheet 6Sheet 7Sheet 8Sheet 9Sheet 10Sheet 11
Sheet 1Sheet 2Sheet 3Sheet 4Sheet 5Sheet 6Sheet 7Sheet 8Sheet 9Sheet 10Sheet 11
Literature
- Heuser, Funktionalanalysis, Teubner
- Meise, Vogt, Einführung in die Funktionalanalysis
- Schröder, Funktionalanalysis, Akademie Verlag
- Mathieu, Funktionalanalysis, Spektrum
- Rudin, Functional Analysis, McGraw-Hill