Funktionalanalysis, Wintersemester 2020-21

Previous announcements (no longer relevant)

• 9.02.2021: Problem 1(j) on Problem Set 10 has been cancelled due to an error in the statement of the main result about the Laplace operator on bounded domains. (Update 11.02: A revised version of the lecture notes on Fredholm operators has now been posted above to correct the errors.)
• 7.01.2021: There was a missing hypothesis in the original version of Problem 2 on Problem Set 8: the function ρ should be assumed nonnegative. (This has been corrected in the version below.)
• 17.12.2020: The take-home midterm will be assigned on January 21 and due Feburary 4. (Regular problem sets will not be assigned in those two weeks.)
• 9.12.2020: If you downloaded Problem Set 6 within a few hours of when it first appeared (on the evening of 9.12), you may have a version that is missing an important hypothesis in Problem 4. It has been corrected in the version available below, so make sure you press the reload button to get the corrected version. (This will be irrelevant to the vast majority of you, who surely did not look at Problem Set 6 before Problem Set 5 was even due. But at least one person did.)
• 29.11.2020: A small typo in the hint for Problem Set 4 #4(b) has now been corrected in the version posted below (and also on the moodle).
• 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.) Update: The course will be run in English.
• 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.