We consider scattering by short range perturbations of the semi-classical Laplacian. We prove that when a polynomial bound on the resolvent holds the scattering amplitude is a semi-classical Fourier integral operator associated to the scattering relation near a non-trapped ray. Compared to previous work, we allow the scattering relation to have more general structure.

The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix is shown to determine the asymptotics of a large class of perturbations.

Fundamental solution for a Schrödinger equation with a time-dependent potential of long-range type is constructed. The solution is given as a Fourier integral operator with a symbol uniformly bounded global in time, when measured in natural semi-norms of a symbol class.

We provide a polynomial decay rate for the energy of the wave equation with a dissipative boundary condition in a cylindrical trapped domain. A new kind of interpolation estimate for the wave equation with mixed Dirichlet-Neumann boundary condition is established from a construction based on a Fourier integral operator involving a good choice of weight functions.

The present paper deals with the wavelet transform of fractional integral operator (the RiemannLiouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

In this paper, we deal with the problems of expansions periodic distributions. We obtained sufficient conditions for equiconvergence spectral decompositions distributions connected elliptic differential operator on torus Fourier integral in classes Sobolev.

Fourier integral operators, for the calculus of which I refer to Hörmander [17], have been applied in essentially two ways: as similarity transformations and in the description of the solutions of genuinely nonelliptic (pseudo-) differential equations. The first application is based on the observation of Egorov [12] that if P9 resp. g, is a pseudo-differential operator with principal symbol equ...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.