250019 VO Functional Analysis (2026S)
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An/Abmeldung
Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
Details
Sprache: Englisch
Prüfungstermine
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
- Dienstag 03.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 05.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 10.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 17.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 19.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 24.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 26.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 14.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 16.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 21.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 23.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 28.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 30.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 05.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 07.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 12.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 19.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 21.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 26.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 28.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 02.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 09.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 11.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 16.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 18.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 23.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 25.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Dienstag 30.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
Topics: Locally convex spaces; Weak topologies; Compactness and reflexivity; Extreme points; Density of algebras of continuous functions; Spectral theorems and functional calculi for normal bounded operators (continuous and Borel calculi); Joint diagonalization of commuting operators; Unbounded operators; Spectral theorem for self-adjoint unbounded operators; Several applications, including distributions (generalized functions); Banach algebras and C* algebras.Prerequisites: bachelor level knowledge about point-set topology (including product topologies, nets and compactness); functional analysis (including Banach spaces and linear operators); and measure theory (including abstract measures, Fubini, Radon-Nikodym and the Hahn decomposition).Participation in the accompanying problem seminar is strongly advised.
Art der Leistungskontrolle und erlaubte Hilfsmittel
Written or oral exam on the entire course material (consultation with colleagues, books, notes or the internet during the exam is not allowed).Exam dates:
- July 2, 2026 (enrollment from June 15 to June 19, 2026)
- October 1, 2026 (enrollment from September 14 to September 18, 2026)
- December 10, 2026 (enrollment from November 23 to November 27, 2026)
- January 28, 2027 (enrollment from January 11 to January 15, 2027)To enroll, please write an email to the teacher within the specified enrollment period and with the subject "Enrollment Exam Functional Analysis". You will then receive a time slot.
- July 2, 2026 (enrollment from June 15 to June 19, 2026)
- October 1, 2026 (enrollment from September 14 to September 18, 2026)
- December 10, 2026 (enrollment from November 23 to November 27, 2026)
- January 28, 2027 (enrollment from January 11 to January 15, 2027)To enroll, please write an email to the teacher within the specified enrollment period and with the subject "Enrollment Exam Functional Analysis". You will then receive a time slot.
Mindestanforderungen und Beurteilungsmaßstab
Assessment criteria: quality of answers to questions about course and solution of problems.
Minimum requirements: detailed knowledge of course material and its applications. To pass, at least half of the questions need to be answered correctly. Illustrative list of grades: 88-100 sehr gut; 75-87 gut; 62-74 befriedigend; 50-61 genuegend; <50 nicht genuegend
Minimum requirements: detailed knowledge of course material and its applications. To pass, at least half of the questions need to be answered correctly. Illustrative list of grades: 88-100 sehr gut; 75-87 gut; 62-74 befriedigend; 50-61 genuegend; <50 nicht genuegend
Prüfungsstoff
Entire course material. The lecture notes and the exercise sheets - both available on the Moodle website of the lecture - help students to prepare for the exam. The Moodle website also provides many additional supporting materials and background information.
Literatur
Main literature
* Conway, John B. A course in functional analysis. Second edition. Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990.
* Reed, Michael; Simon, Barry Methods of modern mathematical physics. I. Functional analysis. Academic Press, New York-London, 1972.
Complementary literature
* Brezis, Haim Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.
* Yosida, Kôsaku Functional analysis. Sixth edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 123. Springer-Verlag, Berlin-New York, 1980.Also: lecture notes available on the Moodle website of the lecture.
* Conway, John B. A course in functional analysis. Second edition. Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990.
* Reed, Michael; Simon, Barry Methods of modern mathematical physics. I. Functional analysis. Academic Press, New York-London, 1972.
Complementary literature
* Brezis, Haim Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.
* Yosida, Kôsaku Functional analysis. Sixth edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 123. Springer-Verlag, Berlin-New York, 1980.Also: lecture notes available on the Moodle website of the lecture.
Zuordnung im Vorlesungsverzeichnis
MANF; ML1; MEL
Letzte Änderung: Fr 02.10.2026 08:47