Applications to the Solutions of Analytic Linear PDEs

Abstract

The purpose of this chapter is to apply the results of the previous sections for finding out many microlocal properties of the L ²-solutions of partial differential equations of the type

$$P(x,h{D_x})u = 0,$$

where $P = \sum\limits_{|a| \leqslant m} {{a_\alpha }} (x)(h{D_x})\alpha$ has analytic coefficients. In particular, properties of localization and propagation are given for the microsupport MS(u) when u is normalized by $||u|{|_{{L^2}}} = 1$.