syllabus

homework

problems

latex

6616 course notes

6617 course notes

• Friday 20 April. Finished Section 26.5 and covered Section 26.6.
• Wednesday 18 April. Began Section 26.5 up through Proposition 26.12.
• Notes updated Monday 16 April at 1pm. Reworked the proof of Proposition 26.8 plus typo patrol.
• Monday 16 April. Finished section 26.3 and covered Section 26.4.
• Notes updated Friday 13 April at 1:50 pm. Fixed typos in Sections 26.2 and 26.3.
• Friday 13 April. Homework 11 is was due. Subsection 26.2 up through Proposition 26.6.
• Wednesday 11 April. Began Section 26, covering up through Proposition 26.2.
• Monday 9 April. Finished Section 25.4, starting with Lemma 25.39.
• Notes updated Friday 6 April at 8:20 pm. Fixes and upgrades in Section 25.4.
• Friday 6 April. Continued in Section 25.4, from Proposition 25.35 through Corollary 25.38.
• Wednesday 4 April. Homework 10 was due. Covered Section 25.4 up through Theorem 25.34.
• Notes updated Monday 2 April. Simplified the proof of Theorem 25.30, fixed some typos plus a few small upgrades.
• Monday 2 April. Finished Section 25.3 and began Section 25.4.
• Friday 30 March. Finished Section 25.2 by discussing the proofs of Proposition 25.25 and Fourier Inversion. Began Section 25.3 by discussing Lemma 25.28.
• Notes updated 29 March at 2:30pm. Typos fixed, expository upgrades, an update to Problem 25.8 and Problem 25.25 added.
• Wednesday 28 March, homework 9 was due. Finished Section 25.1 and covered up through the statement of Proposition 25.25.
• Monday 26 March. Section 25.1 up through Lemma 25.18.
• Friday 23 March. Professor Brooks – introduction to Brownian motion.
• Wednesday 21 March. More of Section 25, from the proof of 25.8 through Lemma 25.12.
• Notes updated Wednesday 21 March at 9:05am. Typos patrol.
• Friday 2 March. Finished the proof of Theorem 24.13 in the case of finite measures.
• Monday 19 March. Homework 8 was due. Began Section 25 up through the statement of Proposition 25.8.
• Friday 16 March. Section 24.5.
• Wednesday 14 March. Proved that simple functions are dense in Lp, Lp is reflexive and continuous functions of compact support are in Lp.
• Monday 12 March. Finished the proof of Theorem 24.13.
• Notes updated Friday 2 March at 5:35pm. Many typos fixed and improvements made, including spelling out exactly when equality holds in Holder’s inequality.
• Wednesday 28 February. Continued in Section 24, from the proof of Young’s inequality part way through the proof of Lp-Lq duality (Theorem 24.13).
• Monday 26 February. Homework 7 was due. Began Section 24 up through the statement of Young’s inequality.
• Friday 23 February. Theorem 23.41 (finishing Section 23) and discussed Problem 23.6 on Fourier Series.
• Wednesday 21 February. Nearly finish Section 23.
• Monday 19 February. Homework 6 was due. Continued in Section 23.10 up through Theorem 23.34.
• Friday 16 February. Section 23.10 up through (most of) Theorem 23.32.
• Notes updated Wednesday 14 February at 2:50pm. Fixed the proof of Theorem 23.22.
• Wednesday 14 February. Homework 5 was due. Finished Section 23.8.
• Monday 12 February. Section 23.7 and Section 23.8 up through Proposition 23.21.
• Notes updated Sunday 11 February. Some upgrades and typos fixed in Sections 23.7 and 23.8.
• Friday 9 February. Homework 4 was due. Finished Section 23.6.
• Wednesday 7 February. Sections 23.5 and up through the statement of 23.14 in Section 23.6.
• Notes updated Sunday 4 February at 4:10pm. Typos fixed and small upgrades through Section 23.5.
• Monday 5 February. Sections 23.3 and 23.4
• Friday 2 February. Sections 23.1 and 23.2.
• Wednesday 31 January. The closed graph theorem.
• Monday 29 January. Homework 3 was due. The open mapping theorem.
• Friday 26 January. Homework 2 was due. Continue in Section 22 starting. from the PUB to Lemma 22.5 plus Problem 22.5.
• Wednesday 24 January. Finished Section 21, starting with Proposition 21.16. Began Section 22 up through the proof of the Baire Category Theorem.
• Notes updated Monday 12 January at 1:45pm. Typo patrol and a few small expository upgrades.
• Monday 22 January. Theorem 21.14 and Proposition 21.15.
• Friday 19 January. More of Section 21, from Theorem 21.9 through Definition 21.12.
• Wednesday 17 January. Continued in Section 21, from the real version of the Hahn-Banach Theorem through Proposition 21.8.
• Friday 12 January. Homework 1 was due. Continued in Section 21, from the proof of Proposition 21.1 through the statement of Zorn’s Lemma.
• Notes updated Thursday 11 January. Typos fixed up through Corollary 21.8. Added the statement of Zorn’s lemma.
• Wednesday 10 January. Finished Section 20 and began Section 21 up through the statement of Proposition 21.1.
• Monday 8 January. A bit of review and Propositions 20.8 and 20.9.