We establish observability inequalities for various p roblems involving fractional Schrödinger operators (−Δ)α/2 + V, α > 0, on a compact Riemannian manifold. Observability from an open set the corresponding evolution equation with 1 is proved to hold as soon observation satisfies Geometric Control Condition; it also shown that this condition necessary when manifold d-dimensional sphere equippe...

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests in recent years. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory (see e.g...

We consider unitary analogs of d−dimensional Anderson models on l2(Zd) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates o...