Operator Calculus and Spectral Theory

InhaltsverzeichnisHeat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary.Recurrent versus diffusive quantum behavior for time-dependent Hamiltonians.Perturbations of spectral measures for Feller operators.A global approach to the location of quantum resonances.On estimates for the eigen-values in some elliptic problems.Quantum scattering with long-range magnetic fields.Spectral invariance and submultiplicativity for Fréchet algebras with applications to pseudo-differential operators and ?* -quantization.Décroissance exponentielle des fonctions propres pour l’opérateur de Kac: le cas de la dimension > 1.Second order perturbations of divergence type operators with a spectral gap.On the Weyl quantized relativistic Hamiltonian.Spectral asymptotics for the family of commuting operators.Pseudo differential operators with negative definite functions as symbol: Applications in probability theory and mathematical physics.One-dimensional Schrödinger operators with high potential barriers.General boundary value problems in regions with corners.Some results for nonlinear equations in cylindrical domains.Global representation of Langrangian distributions.Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges.Maslov operator calculus and non-commutative analysis.Relative time delay and trace formula for long range perturbations of Laplace operators.Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds.The variable discrete asymptotics of solutions of singular boundary value problems.Schrödinger operators with arbitrary non-negative potentials.Abel summability of the series of eigen- andassociated functions of the integral and differential operators.The relativistic oscillator.On the ratio of odd and even spectral counting functions.A trace class property of singularly perturbed generalized Schrödinger semi-groups.Radiation conditions and scattering theory for N-particle Hamiltonians (main ideas of the approach).