Philip T. Gressman
J. W. Gibbs Assistant Professor
Department of Mathematics
Yale University

402 Dunham Lab

Office Hours:
Tu 3:00pm-4:00pm
We 5:30pm-6:30pm
or by appt.

This is my third year at Yale. Previously, I was a graduate student at Princeton; my thesis advisor is Elias M. Stein. Before that, I was an undergraduate at Washington University in St. Louis, advised by Guido Weiss and Edward N. Wilson. My main interests lie in harmonic analysis and geometric measure theory.

Fall 2007 Course

Math 744a: Introduction to Fourier Analysis on Euclidean Spaces
Meets TTh 1:00-2:15 in LOM 215.
This course is intended to serve as an introduction to the Fourier restriction problem and the Bochner-Riesz conjecture. The only prerequisites are familiarity with measure theory and Lebesgue spaces. Topics to be covered along the way include tempered distributions, the Fourier transform, harmonic functions, basic operator theory (including multipliers and interpolation), Calderon-Zygmund theory, and Littlewood-Payley theory.

  1. Lecture notes (updated 10/30/07).
  1. Uniform estimates for cubic oscillatory integrals. arXiv:0707.2557v2 (submitted).
  2. Rank-type $L^p-L^q$ and Sobolev estimates for averages over submanifolds.

  1. Sharp $L^p-L^q$ estimates for generalized $k$-plane transforms. (to appear in Adv. Math.)
  2. $L \sp p$-improving properties of X-ray like transforms. Math. Res. Lett.. 13 (2006), no 5, 787-803 [.pdf]
  3. (with E. M. Stein) Regularity of the Fourier transform on spaces of homogeneous distributions. Journal d'Analyse Mathematique. 100 (2006) 211-222 [.pdf]
  4. Convolution and fractional integration with measures on homogeneous curves in $\Bbb R\sp n$. Math. Res. Lett. 11 (2004), no. 5-6, 869-881. [.pdf]
  5. (with D. Labate, G. Weiss, and E. N. Wilson) Affine, quasi-affine and co-affine wavelets. Beyond wavelets, 215-223, Stud. Comput. Math., 10, Academic Press/Elsevier, San Diego, CA, 2003. [.pdf]
  6. Wavelets on the integers. Collect. Math. 52 (2001), no. 3, 257-288. [.pdf]