Math 247B (Harmonic Analysis).
Lectures: MWF 10:00-10:50am in MS 6627.
Instructor: Monica Visan, MS 6167. Email address: email@example.com
Office Hours: Tu 1:30-2:30pm and Fri 1:30-2:30pm in MS 6167.
- Concentration compactness for the Gagliardo-Nirenberg and Sobolev
- Existence of optimizers for Sobolev embedding.
- The Kakeya problem.
- Restriction theory beyond L2.
- Concentration compactness for the Schrodinger propagator.
- Optimizers for the Strichartz inequality.
- J. Bourgain, Besicovitch
type maximal operators and applications to Fourier analysis. GAFA 1 (1991), 147-187.
- R. Killip and M. Visan, Nonlinear
Schrodinger equations at critical regularity. To appear in Clay
Mathematics Institute Summer School Proceedings.
- E. Stein, Harmonic analysis: real-variable methods,
orthogonality, and oscillatory integrals. Princeton Mathematical
Series, 43. Princeton University Press, 1993.
- T. Tao, Restriction theorems
- T. Wolff, Lectures
on harmonic analysis. University
Lecture Series, 29. American Mathematical Society, Providence, RI, 2003.
Grading: Grading will be based solely on the homework. Problems
will be assigned and collected throughout the quarter.
Homework: You may collaborate on the homework, but solutions need
to be written up in your own words.
- Homework 1 is due in class on Monday, Feb.
- Homework 2 is due in my mailbox by 6pm
on Tuesday, March 19th.