Operatori pseudo-differenziali anisotropi su varietà fogliettate
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....
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...
The Penrose transform gives an isomorphism between the kernel of the -Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.