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arXiv · 1505.01566

Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n

A. Ascanelli·S. Coriasco
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Abstract

We study the composition of an arbitrary number of Fourier integral operators $A_j$, $j=1,\dots,M$, $M\ge 2$, defined through symbols belonging to the so-called SG classes. We give conditions ensuring that the composition $A_1\circ\cdots\circ A_M$ of such operators still belongs to the same class. Through this, we are then able to show well-posedness in weighted Sobolev spaces for first order hyperbolic systems of partial differential equations with coefficients in SG classes, by constructing the associated fundamental solutions.

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A. Ascanelli, S. Coriasco. 2015-05-06. Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n. https://doi.org/10.1007/s11868-015-0132-x

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