Geometric proofs of composition theorems for generalized Fourier integral operators.
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Global time estimates for solutions to equations of dissipative type
Global time estimates of norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.
Hyperbolic equations with non-Lipschitz coefficients.
-boundedness and -compactness of a class of Fourier integral operators.
Local Riesz transform characterization of local Hardy spaces
Lp - Lp'-Estimates for Fourier Integral Operators Related to Hyperbolic Equations.
Micro-Local Analysis in Some Spaces of Ultradistributions
Normal forms of real symmetric systems with multiplicity
On oscillatory integral operators with folding canonical relations
Sharp estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation projects to T*X and T*Y with fold singularities.
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the range of the Fourier transform connected with Riemann-Liouville operator
We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
Opérateurs intégraux de Fourier et calcul de Weyl-Hörmander (cas d'une métrique symplectique)
Oscillatory and Fourier integral operators with degenerate canonical relations.
We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Oscillatory integrals with polynomial phases.
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
Pseudodifferential operators with generalized symbols and regularity theory.
Recent progress in the regularity theory of Fourier integrals with real and complex phases and solutions to partial differential equations
In this paper we will give a brief survey of recent regularity results for Fourier integral operators with complex phases. This will include the case of real phase functions. Applications include hyperbolic partial differential equations as well as non-hyperbolic classes of equations. An application to an oblique derivative problem is also given.
Resolvent and Scattering Matrix at the Maximum of the Potential
2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing...
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.