Magnetic Bi-harmonic differential operators on Riemannian manifolds and the separation problem

摘要

In this paper we obtain sufficient conditions for the bi-harmonic differential operator A = Delta(E) (2) + q to be separated in the space L (2) (M) on a complete Riemannian manifold (M,g) with metric g, where Delta(E) is the magnetic Laplacian onM and q aeyen 0 is a locally square integrable function on M. Recall that, in the terminology of Everitt and Giertz, the differential operator A is said to be separated in L (2) (M) if for all u a L (2) (M) such that Au a L (2) (M) we have Delta(E) (2) u a L (2) (M) and qu a L (2) (M).