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- and associated 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).