## Tsukuba Journal of Mathematics

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

Marco Cappiello

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 28, Number 2 (2004), 311-361.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164804

Digital Object Identifier
doi:10.21099/tkbjm/1496164804

Mathematical Reviews number (MathSciNet)
MR2105940

Zentralblatt MATH identifier
1079.35108

#### Citation

Cappiello, Marco. Fourier integral operators of infinite order and applications to SG-hyperbolic equations. Tsukuba J. Math. 28 (2004), no. 2, 311--361. doi:10.21099/tkbjm/1496164804. https://projecteuclid.org/euclid.tkbjm/1496164804