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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.

MSC:
 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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