Ankündigungen / Announcements

• 7.01.2020: 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.)
• 17.12.2020: The two dates for the final exam in this course have now been fixed. They are:
  • Wednesday, 3.03.2021 from 9:00 to 12:00
  • Friday, 9.04.2021 from 9:00 to 12:00
  For both dates, the exam will be a take-home exam that is made available via the moodle at 9:00 sharp, with 12:30 as the deadline for uploading solutions. (The extra half-hour is added as a buffer in case of technical problems.) The exam problems will be conceived to be doable within two hours, so time pressure should not be a major factor. The deadline to register with the Prüfungsbüro is (as usual) 14 days ahead of the exam. For information on administrative matters such as how to register, here is the webpage of the Prüfungsbüro Mathematik.
• 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.)

Übungsblätter / Problem sets

Problem sets will normally be posted in this spot every Thursday and can be submitted via the moodle until 15:15 on the following Thursday; solutions will then be discussed in the Übung. (See the moodle for more on the technical details of how to submit solutions.) You are welcome to work on the problems in groups, but must write up solutions (in German or English) individually -- group submissions are not accepted.

The corrected submissions are posted on the moodle about a week after the due date. Questions about the grading can be directed to the grader, Laurenz Upmeier zu Belzen (upmeibel at mathematik dot hu dash berlin dot de).

• Probelm Set 1 (due 12.11.2020)
• Problem Set 2 (due 19.11.2020)
• Problem Set 3 (due 26.11.2020)
• Problem Set 4 (due 3.12.2020)
• Problem Set 5 (due 10.12.2020)
• Problem Set 6 (due 17.12.2020)
• Problem Set 7 (due 7.01.2021)
• Problem Set 8 (due 14.01.2021)
• Problem Set 9 (due 21.01.2021)

Other useful links

• notes by Keith Conrad on finite-dimensional topological vector spaces (see Theorem 2.7 for a proof that the topology is unique)
• Eric Schechter's book Handbook of Analysis and its Foundations contains an exhaustive discussion of the role played by the Axiom of Choice in functional analysis, including an outline of the proof that it is equivalent to Zorn's lemma, and informal explanations of surprising facts like the impossibility of constructing explicit examples of unbounded linear operators. Schechter's webpage on the Axiom of Choice is also an entertaining read.
• For a direct proof that Zorn's lemma and the Axiom of Choice are equivalent, see Appendix A in Bühler-Salamon.
• Fourier series graph interactive (Java applet)
• Fourier version 1.0 by Paul Falstad (Java applet)