Università Roma Tre

1. Theory of distributions

Definition and convergence of distributions.
Derivative of a distribution.
Spaces of distributions.
Convolutions.
Schwartz space, tempered distributions.
Fourier transform of tempered distributions.
Sobolev spaces and pseudo-differential operators.

2. Application to Schrödinger equations

Linear Schrödinger equation, local and global smoothing effects.
Nonlinear Schrödinger equation, local theory in L^2, H^1, H^2.
Asymptotic results and singularity formation for NLS.

Bony - Cours d'analyse, Théorie des distributions et analyse de Fourier
Ponce, Linares - Introduction to nonlinear dispersive equations