Schedule of classes : T R 9:45 - 11:00 AM in 107 WILLARD.
NO CLASSES OCTOBER 2-4, 2012.
EXTRA CLASSES: Tuesday September 18 and Tuesday December 11.
Both sessions held 5:30 - 6:45 PM in 315 McAllister.
Office Hours (subject to change):
TUESDAY 11 AM - 12:30 PM,
THURSDAY 5 - 6:30 PM.
Textbook (optional) J. Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.
Course Topics :
- Fourier series and Fourier transform in $L^{1}$ and $L^{2}$: basic properties, inversion, summability methods (Gauss-Weierstrass, Abel), point-wise convergence (briefly);
- Schwartz space, tempered distributions, weak derivatives (review), principal-value distributions, Fourier transform on distributions;
- Interpolation of operators: weak $L^{p}$, Marcinkiewicz and Riesz-Thorin Theorems;
- Hardy-Littlewood maximal function and Calderon-Zygmund decomposition (via dyadic maximal function);
- Hilbert transform and Fourier multipliers on the real line;
- Singular integrals: convolution operator with odd homogeneous kernels, Riesz transforms, and method of rotations;
Homework Problems: solutions will be available on ANGEL ( under the "lessons" tab) roughly one week after the problems are posted.
- Homework 1, due THURSDAY SEPTEMBER 20.
- Homework 2, due THURSDAY OCTOBER 11.
- Homework 3, due THURSDAY OCTOBER 25.
- Homework 4, due THURSDAY NOVEMBER 8.
- Homework 5, due THURSDAY NOVEMBER 29.
- Homework 6, due TUESDAY DECEMBER 11.
© Anna Mazzucato Last modified: Tue Dec 4 12:20:52 EST 2012