Microlocal Analysis and Spectral Theory

The NATO Advanced Study Institute "e;Microlocal Analysis and Spectral The- ory"e; was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "e;11 Ciocco"e; , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa- tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin- ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math- ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.