PSU
Mark
Eberly College of Science Mathematics Department

Math 504 - Fall 2015
              Analysis on Euclidean Space


Schedule of classes : T R 11:15 AM - 12:30 PM in 009 WALKER.

PLEASE NOTE, THIS COURSE WILL MEET IN 315 MCALLISTER INSTEAD OF THE OFFICIAL CLASSROOM (9 WALKER).



Office Hours (subject to change): TUESDAY 5-6:30 PM THURSDAY 1-2:30 PM


Syllabus.



Textbook (optional) J. Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.
Fulltext can be downloaded from PSU library: http://www.ams.org.ezaccess.libraries.psu.edu/books/gsm/029/.

Course Topics :
  1. Fourier series and Fourier transform in $L^{1}$ and $L^{2}$: basic properties, inversion, summability methods (Gauss-Weierstrass, Abel), point-wise convergence (briefly);
  2. Schwartz space, tempered distributions, weak derivatives (review), principal-value distributions, Fourier transform on distributions;
  3. Interpolation of operators: weak $L^{p}$, Marcinkiewicz and Riesz-Thorin Theorems;
  4. Hardy-Littlewood maximal function and Calderon-Zygmund decomposition (via dyadic maximal function);
  5. Hilbert transform and Fourier multipliers on the real line;
  6. Singular integrals: convolution operator with odd homogeneous kernels, Riesz transforms, and method of rotations;
Additional topics if time allows : generalized Calderon-Zygmund singular integrals, pseudo-differential operators, Littlewood-Paley theory and applications to non-linear PDEs, Hardy spaces and BMO.



Homework Problems: solutions will be available on ANGEL/CANVAS roughly one week after the problems are posted.
You can access CANVAS via ANGEL or at: https://psu.instructure.com/.




© Anna Mazzucato
Last modified: Sat Aug 22 11:03:25 EDT 2015