- Notes updated Tuesday 4 April at 5:30 pm. Added up through the first half of Section 27.3.
- Monday 3 April. Section 27, up through Theorem 27.3.
- Friday 31 March, Finish section 25.5 and section 26.6.
- Notes Friday 31 March at 9:30 am. Some expository upgrades; additions of Section 26.5 and the start of Section 27.
- Wednesday 29 March Sections 26.4 and 26.5.
- Notes updated 29 March at 7:35 am. Added section 26 – Banach algebras.
- Monday 27 March. Sections 26.2 and 26.3.
- Friday 24 March. Homework 10 is due. Section 26.1.
- Wednesday 22 March. Finish the subsection on Fourier Series.
- Monday 20 March. Fourier Series up through Proposition 25.35.
- Friday 17 March. Homework 9 is due. Return to the Fourier transform: a brief review through the end of Section 25.3.
- Notes updated 16 March at 2:35 pm. Typos fixed. Small improvements from Theorem 25.29 through the end of subsection 25.3.
- Monday and Wednesday 13 and 15 March. Professor Jury will substitute.
- Friday 3 March. Continued in Section 25, from Lemma 25.23 through Theorem 25.29.
- Notes updated 3 March at 9:15 am. Typos fixed and small upgrades in Section 25 up through the proof of Lemma 25.28.
- Wednesday 1 March. More of Section 25, starting with the proof of Theorem 25.17 through the statement of the L1 case of Fourier inversion.
- Monday 27 February. Proposition 25.11 and Proposition 25.14 through the proof of Lemma 25.18.
- Notes updated 27 February at 10:30 am. Typos fixed in Section 25 up through Section 25.1
- Friday 24 February. Homework 8 was due. More of Section 25, from Proposition 25.6 through Proposition 25.13.
- Wednesday 22 February. Began Section 25 up through Lemma 25.5.
- Monday 20 February. Remark 24.16 and Section 24.5.
- Friday 17 February. Homework 7 was due. Finished the proof of Theorem 24.13. Corollary 24.17.
- Notes updated Friday 17 February at 10:30 am. Expository improvements and a few typos fixed in Sections 24.1 and 24.5.
- Wednesday 15 February. More of Section 24, from the proof of Holder’s inequality through the middle of the proof of Theorem 24.13.
- Monday 13 February. Continued in Section 24, from Remark 24.3 through the proof of Young’s inequality.
- Friday 10 February. Homework 6 was due. Finished Section 23. Began Section 24 up through Proposition 24.2.
- Wednesday 8 February. Finished Section 23.10 and began Section 23.11 up through the definition of weak convergence in separable Hilbert space.
- Notes updated Wednesday 8 February at 9:50 am. More expository upgrades and typos fixed in Section 21.10.
- Monday 6 February. Theorem 23.31 and Proposition 23.32.
- Notes updated Friday 3 February at noon. Some expository upgrades and typos fixed in Section 21.10.
- Friday 3 February. Homework 5 was due. Section 23.10, through Theorem 23.30.
- Wednesday 1 February. Theorem 23.21 through Example 23.25.
- Monday 30 January. Finished the proof of the Reisz Representation Theorem. Began Section 23.8 and discussed Problems 23.2 and 23.3.
- Notes updated Monday 30 January at 9:40 am. Typos fixed in Sections 23.7 and 23.8, particularly the proof of the Riesz representation theorem.
- Friday 27 January. Homework 4 was due. Finished Section 23.6. Began Section 23.7.
- Wednesday 25 January. Finished the proof of Theorem 23.3; Section 23.5; and Section 23.6 up through Theorem 23.13.
- Notes updated Wednesday 25 January at 10am. Typos fixed and expository upgrades in Sections 23.1 through 23.5.
- Monday 23 January. Subsections 23.2, 22.3 and 23.4.
- Friday 20 January. Homework 3 was due. Finished Section 22. Begin Section 23 up through the proof of item (i) of Theorem 23.3.
- Notes updated Friday 20 January at 9:55 am. Fixed the statement of Problem 22.2, improved the proof of the closed graph theorem and typo patrol at the last bit of Section 22.
- Wednesday 18 January. Continue in Section 22 starting with the proof of Lemma 22.5 through Corollary 22.7, plus an outline of Problem 22.10.
- Notes updated Wednesday 18 January at 10:15 am. Expository improvements in the proofs of 22.5 and 22.6.
- Monday 16 January. ML King holiday. No class.
- Friday 13 January. Homework 2 was due. Corollary 22.2, Problem 22.7, Theorem 22.4 (PUB), and an initial discussion of Lemma 22.5.
- Notes last updated 11 January at 4:10. Expository upgrade to treatment of the Baire Cateogry Theorem.
- Wednesday 11 January. Homework 1 was due. Began Section 22 through the proof of the Baire Category Theorem. Also discussed Problems 21.1 and 21.4.
- Notes updated Wednesday 11 January at 10:40 am. Typos fixed and other small changes in the problems and first part of Section 22.
- Monday 9 January. Finish Section 21. Discussed Problem 21.11.
- Friday 6 January. Finished Corollary 21.10 and continued in Section 21 up through Theorem 21.4.
- Notes updated Friday 6 January at 9:50 am. Typos fixed and expository upgrades in section 21.4.
- Wednesday 4 January. Reviewed. The complex version of the Hahn-Banach Theorem (Theorem 21.9) and up through part (iii) of Corollary 21.10.
- Notes updated Wednesday 4 January at 10:30am. Typos fixed and the statement of Proposition 21.8 revised.
|