Math 254B, Spring 1999
Restriction theorems and applications
- Class is at MS 5233, MWF 11, with office hours MWF 12-2.
My office is MS 5622, my e-mail is firstname.lastname@example.org, and my phone is x54984.
- A description of the course.
- Lecture notes 1. Hausdorff-Young, statement of restriction conjecture.
- Lecture notes 2. The Tomas-Stein restriction theorem.
- Lecture notes 3. Bochner-Riesz summation, Fefferman's disc multiplier counterexample.
- Lecture notes 4. The L^2-critical non-linear Schrodinger equation in 2D.
- Lecture notes 5. Two-dimensional restriction theorems, the Kakeya conjecture.
- Lecture notes 6. The Kakeya estimates of
Cordoba, Drury et al., Bourgain, and Wolff. (Errata: In (8) and (9), as well as the display preceding (8), delta should be 1/delta. Thanks to Richard Drysdale for the correction.)
- Lecture notes 7. Using Kakeya estimates to
obtain improvements to Tomas-Stein.
- Lecture notes 8. Bourgain's arithmetical approach to Kakeya, and the conclusion of the course.
Note: These notes are somewhat rough, and likely to have a few minor errors. Corrections are greatly appreciated.
These notes are public domain. Feel free to redistribute them as you wish.
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