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

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.

34 pages

References in corpus (3)

• Calculus, continuity and global wave-front properties for Fourier integral operators on ${\mathbf{R}}^d$
• SG-Lagrangian submanifolds and their parametrization
• Calculus for Fourier Integral Operators in generalized SG classes

Cited by in corpus (2)

• Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients
• Deterministic and Stochastic Cauchy problems for a class of weakly hyperbolic operators on R^n