Fourier integral operators of infinite order and applications to SG-hyperbolic equations

Abstract

In this work, we develop a global calculus for a class of Fourier integral operators with symbols $a(x, \xi)$ having exponential growth in $R_{x,\xi}^{2n}$. The functional frame is given by the spaces of type S of Gelfand and Shilov. As an application, we construct a parametrix and prove the existence of a solution for the Cauchy problem associated to SG-hyperbolic operators with one characteristic of constant multiplicity.