W: Question hour (usual time & place)
Midterm (5-7pm in BA 6183)
F: Weak convergence. Banach-Alaoglu theorem
Week 9 (March 10-14)
The Fourier transform (Lieb & Loss Chapter 5, Folland Chapter 8)
- M: Definition and basic properties.
- W: Construction of the
L2 -Fourier transform.
Parseval's and Plancherel's identities
- F: The Fourier inversion theorem
Assignment 7
(due March 19)
Week 10 (March 17-21)
Distributions (Folland Chapter 9, Lieb & Loss Chapter 6)
- M: The resolvent of the Laplacian.
Hausdorff-Young inequality
- W: Schwarz space and tempered distributions
- F: Distributions and test functions. Weak derivatives
Assignment 8
(due March 26)
Corrections
Week 11 (March 24-28)
Distributions (Folland Chapter 9, Lieb & Loss Chapter 6)
- M: Tempered distributions.
The Fourier transform on S'.
- W: Convolutions; approximation by smooth functions
- F: How to compute distributional derivatives
Assignment 9
(due April 2)
Week 12 (March 31 - April 4)
Sobolev spaces, and a little geometric analysis
(Lieb & Loss Chapter 6; Stein & Shakarchi Section 1.5)
- M: Definition and basic properties.
Statement of the Sobolev inequality for
||grad u|| p
- W: Brunn-Minkowski and isoperimetric inequality
- F: Proof of Brunn-Minkowski
inequality
Assignment 10
(due April 9)
Final Exam: Wednesday, April 9, 2-5pm in Bahen 6183
( Last year's final exam,
qualifying exams)
Presentations: April 16 (Wed. morning),
April 17 (Thu. morning), April 21 (Mon. all day)
Instructions and schedule
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