Funktionalanalysis, Wintersemester 2020-21

Inhaltsbeschreibung / course description and syllabus

WICHTIG: Die Lehrveranstaltung findet online per Zoom statt, und Sie müssen sich beim Moodle-Kurs anmelden, um die Zugangsdaten für die Zoom-Meetings zu erhalten. HU-Angehörige haben mit ihrem HU-Benutzernamen und Passwort automatisch Zugang zum Moodle. Nicht HU-Angehörige haben Zugang, indem sie auf den Link oben klicken und dann ein HU-Moodle-Konto erstellen mit der externen Mailadresse als Benutzername. Aktuell gibt es keinen Einschreibeschlüssel für diese Lehrveranstaltung.
IMPORTANT: The course will be conducted online via Zoom, and you will need to join the moodle for the course in order to obtain the Zoom links for online lectures. HU students can access moodle using their HU username and password. Non-HU users can access it by following the above link and then setting up a HU Moodle Account with their external e-mail address as a username. At the moment there is no enrolment key for this course.

Lecture notes (last update: 20.10.2020)
The current version of the lecture notes includes only Section 0, which covers a mixture of prerequisite material (to be reviewed in the first problem session) and some definitions that will be introduced/reviewed in the first week of lectures. The latter assumes some knowledge of topologies, Fréchet and locally convex spaces, which will also covered in the first week but are not explained in the notes; a good reference for that material is the book by Reed and Simon.
Note: The file behind the link above will be updated routinely during the semester, so you should press the "reload" button to make sure you have the current version.

Whiteboard notes:
The handwritten whiteboard notes from each lecture will be uploaded in this spot as the semester progresses.

Ankündigungen / Announcements

  • 20.10.2020: The language of the course will be decided in the first lecture: by default it will be English unless everyone agrees it should be German. (It will definitely not be Latin.) Anyone who needs to hear it in English but cannot be there right at the beginning should communicate their wishes to us in advance. (The problem session, AKA "Übung", will be run in English in any case.)
  • 20.10.2020: Die Übung in der ersten Woche dient hauptsächlich als Wiederholung von Stoff aus Analysis 1-3, der als Voraussetzung für diese Vorlesung gilt: z.B. der Konvergenzsatz von Lebesgue und seine Anwendung für parameterabhängige Integrale, absolute Konvergenz von Reihen in Banachräumen, und der Banachsche Fixpunktsatz. Ab der zweiten Woche wird die Übung hauptsächlich (aber nicht ausschließlich) auf die wöchentlichen Übungsblätter fokussiert.
    The problem session (Übung) in the first week will be mostly a review of material from Analysis 1-3 that should be considered prerequisite for this course: e.g. the dominated (Lebesgue) convergence theorem and its application toward differentiation under the integral sign, absolute convergence of series in Banach spaces, and the contraction mapping principle (Banach fixed point theorem). From the second week onward, the problem session will be focused more around the weekly problem sets, though not exclusively so.

Übungsblätter / Problem sets

Problem sets will normally be posted in this spot every Thursday and can be submitted via the moodle until the beginning of the Übung on the following Thursday (solutions will be discussed in the Übung).
  • Probelm Set 1 (to appear in the first week)
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