Microlocal analysis and partial differential equations
by
Luigi Rodino
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy

We first review some known results on microlocal analysis, with applications to partial differential equations. New results are then presented about time-frequency localization operators, defined in terms of two fixed windows; in particular we give a complete asymptotic expansion for the symbol of the product. Applications of the corresponding symbolic calculus concern lower bounds for partial differential equations with positive symbols (results obtained in collaboration with E.Cordero). We also report on recent results of F.Nicola, about lower bounds for pseudo-differential operators with multiple characteristics.

Date received: May 9, 2003