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Fourier integral operators of infinite order and applications to SG-hyperbolic equations. (English) Zbl 1079.35108
Summary: We develop a global calculus for a class of Fourier integral operators with symbols \(a(x,\xi)\) having exponential growth in \(\mathbb{R}^{2n}_{x,\xi}\). 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.

35S30 Fourier integral operators applied to PDEs
35L30 Initial value problems for higher-order hyperbolic equations
35A17 Parametrices in context of PDEs
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