PSU
Mark
Eberly College of Science Mathematics Department

Math 504 - Fall 2012
              Analysis on Euclidean Space


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.


Syllabus.



Textbook (optional) J. Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.

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 ( under the "lessons" tab) roughly one week after the problems are posted.
  1. Homework 1, due THURSDAY SEPTEMBER 20.
  2. Homework 2, due THURSDAY OCTOBER 11.
  3. Homework 3, due THURSDAY OCTOBER 25.
  4. Homework 4, due THURSDAY NOVEMBER 8.
  5. Homework 5, due THURSDAY NOVEMBER 29.
  6. Homework 6, due TUESDAY DECEMBER 11.



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© Anna Mazzucato
Last modified: Tue Dec 4 12:20:52 EST 2012