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.
Citation
Marco Cappiello. "Fourier integral operators of infinite order and applications to SG-hyperbolic equations." Tsukuba J. Math. 28 (2) 311 - 361, December 2004. https://doi.org/10.21099/tkbjm/1496164804
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