Operator Calculus and Spectral Theory

Inhaltsverzeichnis

• Heat 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).