A Note on Vector Valued Discrete Schrödinger Operators

The main purpose of this paper is to extend some theory of Schr¨odinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schr¨odinger equations in multidimensional space. To this end, we will provide the detail proves of some basic results that are necessary for further studies in these areas. In addition, we will introduce Titchmarsh- Weyl m− function of these equations and express m− function in term of the resolvent operators.