Dimensions of Solution Spaces of the Schrodinger Equation with Finite Dirichlet Integral on Non-compact Riemannian Manifolds

Аннотация

Exact estimations of dimensions of spaces of bounded solutions of stationary Schrodinger equation with finite Dirichlet integral in terms of massive sets are obtained. It is proved that dimension of spaces of bounded solutions of this equation is not less than number of disjoint qD-massive subsets of manifold. This paper partly extends, the results of A.A. Grigor’yan, A.G. Losev (2017).