In this work, we develop a global calculus for a class of Fourier integral ope-\\rators with symbols $a(x,\xi)$ having exponential growth in $\R^{2n}_{x,\xi}.$ 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.
Fourier integral operators of infinite order and applications to SG-hyperbolic equations
CAPPIELLO, Marco
2004-01-01
Abstract
In this work, we develop a global calculus for a class of Fourier integral ope-\\rators with symbols $a(x,\xi)$ having exponential growth in $\R^{2n}_{x,\xi}.$ 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.
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