The Cauchy problem for degenerate parabolic equations in Gevrey classes
The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols.
The convergence estimates for Galerkin-wavelet solution of periodic pseudodifferential initial value problems.
The density of the area integral in
Let be a harmonic function in the half-plane , . We define a family of functionals , that are analogs of the family of local times associated to the process where is Brownian motion in . We show that is bounded in if and only if belongs to , an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.
The Essential Spectrum of Elliptic Systems of Mixed Order.
The Fast Fourier Transform and the Numerical Solution of One-Dimensional Boundary Integral Equations.
The Fourier integral operators on Hardy spaces associated with Herz spaces
In this paper, it is proved that the Fourier integral operators of order , with , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
The level crossing problem in semi-classical analysis I. The symmetric case
We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The microlocal Landau-Zener formula
The nonrelativistic limit for the Weyl quantized Hamlitonians and pseudo-differential operators.
The normal symbol on Riemannian manifolds.
The Oblique Derivative Problem. I.
The propagation of singularities for pseudo-differential operators with self-tangential characteristics
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The solvability of non solvable operators
The spectral distribution of a globally elliptic operator
The stationary phase method in Gevrey classes and Fourier integral operators on ultradistributions
The symbol of a lagrangian distribution