Class Of Fourier Integral Operators Research Articles

The Wave Group on Asymptotically Hyperbolic Manifolds

We show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of Fourier integral operators. Then we use now standard techniques to analyze its (regularized) trace. We prove that, as in the case of compact manifolds without boundary, the singularities of the regularized wave trace are contained in the set of periods of closed geodesics. We also obtain an asymptotic expansion for the trace at zero.

Sobolev spaces associated to a polyhedron and Fourier integral operations inR n

The theory of the Sobolev spacesH p m (R n) (m∈R,p polyhedron in R 2n)of [BG]is revisited here in the frame of new classes of pseudodifferential operators related to the same polyhedron p.These operators generalize to corresponding classes of Fourier integral operators, for which we present the main lines of a symbolic calculus and results of continuity on the H p m (R n) spaces.

Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle

The uniform asympotic behavior of the scattering amplitude near the forward peak, in the case of classical scattering of waves by a convex obstacle, is derived. A microlocal model is obtained for the scattering operator. This is achieved by use of a parametrix for diffractive boundary problems and by a new study of a class of Fourier integral operators, those with folding canonical relations. A crucial ingredient consists of putting a Fourier integral operator with folding canonical relation into a normal form. The analysis also gives the asymptotic behavior of the normal derivative of the scattered wave on a neighbourhood of the shadow boundary, thus providing a corrected version of the Kirchhoff approximation.