• Problems 8 up, a little late.
• In answer to a question, yes you certainly can use results for class or old homework problems -- just quote them carefully.
• Correction to Problem set 6 -- I had too weak a notion of exhaustion as pointed out by Michael A., Alex and Hans.
• Lecture 11: 18 October, 2011: Homogeneity.
• 15 October, 2011: Lecture 10 up.
• 15 October, 2011: New version of Problems 6 -- the statement is unchanged.
• Problem set 6 up -- complain if you don't like it!
• 13 October, 2011: Discussion of Assignment 1 reorganized I hope to make it easier to see it all. More to follow.
• There was an error, or at least confusion, in the hint to Problem 4. Now clarified I hope.
• Notes for Lecture 9 up
• 12 October, 2011: Hint on Problem 4 in Problem set 5 expanded.
• 7 October, 2011: Problems 5 up.
• 6 October, 2011: Hint for Question 3 further expanded! Later: the hint further clarified (I hope) after a question from Jonathan.
• 6 October, 2011: Biggish hint added to question 3 on Problem set 4.
• 5 October, 2011: Notes for Lecture 7 finally up.
• Another revision of Problem set 4, signs fixed, typos and constants.
• 4 October, 2011: First shot at assignments below.
• 2 October, 2011: I made Problem set 4 too hard, basically by assuming you knew the Riesz representation theorem for measures. There is a new version with quite a few changes -- I will check it when I get a chance later, so if you have questions let me know.
• 1 October, 2011: Unproofread notes for Lecture 6 up.
• 1 October, 2011: Problem set 4 up. This is about measures and is just supposed to force you to look back at various proofs.
• Lecture 6: Derivatives of distributions, inclusion of integrable functions, Sobolev spaces, convolution.
• 24 September, 2011: Typos in Problems3 fixed.
• 22 September, 2011: Typo in Problem 3 of Problems2.
• 22 September, 2011: Problems 3 up.
• 22 September, 2011: Lecture 5 up.
• 21 September, 2011: Notes for Lecture 4 up. Lecture 5, tomorrow, continuing brief discussion of Lebesgue integration.
• 19 September, 2011: You should have your first homework back now with Nikhil's grading. Feel free to ask questions (of him or me).
• 17 September, 2011: Small typo fixed in Problems Set 2, problem 1.
• 17 September, 2011: Problem set 2 up -- a little late. Please report errors, typos and obscurities!
• 15 September, 2011: Jelena pointed out that the link to the old lecture notes was broken -- it should be fixed now and a reorganized version of the notes should appear soon.
• Lecture 3: 15 September, Fourier transform is an isomorphism on Schwartzz test functions -- division lemma. Maybe embedding test functions in distributions, operations on distributions by duality.
• Lecture 2: 13 September. Topology of the space of Schwartz test functions -- metric and continuity of linear maps. Definition of tempered distributions, examples. Just started Fourier transform.
• The diagnostic test convinced me to include at least a couple of lectures on Lebesgue integration. I will continue discussing Schwartz space of test functions, then define tempered distributions and examine some of their elementary properties and at that point digress with a discussion of Lebesgue integration. Full syllabus up soon. 10 September, 2011.
• Problems 1 up (and revised). 10 September, 2011
• 8 diagnostic tests received. Comments to follow. 10 September, 2011.