Operatori pseudo-differenziali anisotropi su varietà fogliettate
Operators on eigenmaps between spheres
Optimal heat kernel bounds under logarithmic Sobolev inequalities
Optimal heat kernel bounds under logarithmic Sobolev inequalities
We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators of the type Laplacian minus the gradient of a smooth potential with a given growth at infinity....
Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
We consider the wave and Schrödinger equations on a bounded open connected subset of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset of during a time interval with . It is well known that, if the pair satisfies the Geometric Control Condition ( being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...
Oscillatory Integrals and the Method of Stationary Phase in Infinitely Many Dimensions, with Applications to the Classical Limit of Quantum Mechanics. I.
Oscillatory integrals associated to folding canonical relations
Oб одной задаче Кона-Ниренберга.