Open AccessA Note on Vector Valued Discrete Schrödinger Operators
Author(s) -
Keshav Raj Acharya
Publication year - 2016
Publication title -
the nepali mathematical sciences report
Language(s) - English
Resource type - Journals
ISSN - 2392-411X
DOI - 10.3126/nmsr.v34i1-2.29980
Subject(s) - dimension (graph theory) , resolvent , mathematics , operator (biology) , operator theory , algebra over a field , function space , term (time) , function (biology) , pure mathematics , space (punctuation) , vector valued function , mathematical analysis , computer science , physics , quantum mechanics , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene , operating system
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.