Algebraically independent generators of invariant differential operators on a symmetric cone.
Algebras of pseudodifferential operators on complete manifolds.
Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.
Almost classical solutions of Hamilton-Jacobi equations.
Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.
Almost product structures and Monge-Ampère equations.
Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.
An accuracy improvement in Egorov's theorem.
We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in Sm/Sm-1 for the pseudodifferential operators, one uses refined principal symbols in Sm/Sm-2, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally...
An addition theorem for the manifolds with the Laplacian having discrete spectrum.
An analytic proof of Novikov's theorem on rational Pontrjagin classes
An application of the Bakry-Émery criterion to infinite dimensional diffusions
An arithmetic Hilbert–Samuel theorem for pointed stable curves
Let be an arithmetic ring of Krull dimension at most and a pointed stable curve. Write . For every integer , the invertible sheaf inherits a singular hermitian structure from the hyperbolic metric on the Riemann surface . In this article we define a Quillen type metric on the determinant line
An arithmetic Riemann-Roch theorem in higher degrees
We prove an analog in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
An Elementary Proof for a Compact Imbedding Result in Generalized Electromagnetic Theory.
An elementary theory of hyperfunctions and microfunctions
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics
This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result of this...
An estimate for a fundamental solution of a parabolic equation with drift on a Riemannian manifold.
An estimate on the hessian of the heat kernel
An Example on the Heisenberg Group Related to the Levy Operator.
An explicite description of harmonic measure.