Pseudodifferential operators, Fourier integral operators, and microlocal analysis.

1. Short Course on Pseudodifferential Operators (Four Lectures at MSRI)

2. Pseudodifferential Operators and Nonlinear PDE

3. Noncommutative microlocal analysis

4. Boundary Problems for Wave Equations with Grazing and Gliding Rays (with R. Melrose)Click here for figures used in the text.

5. Fourier integral operators and harmonic analysis on compact manifolds

6. Diffraction effects in the scattering of waves

7. Airy operator calculus

8. Lp bounds on functions of generalized Laplacians on a compact manifold with boundary

9. Hardy spaces and bmo on manifolds with bounded geometry

10. Microlocal analysis and nonlinear PDE (MIT conference, 1995)

11. Notes on the Weyl calculus

12. The “Oscillator-Dirac” operator (paradigm with index one) on Euclidean space, and related operators on the Heisenberg group

13. Smooth operators for principal series representations — microlocal properties

14. Commutator estimates for Holder continuous and bmo-Sobolev multipliers.

(See also here for an interpolation result used in the commutator paper.)

15. Microlocal analysis on Morrey spaces

16. Szego projectors and Cauchy integrals on piecewise smooth functions with jumps

17. Asymptotics for some non-classical conormal distributions whose symbols contain negative powers of log |xi|