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Full-Text Articles in Physical Sciences and Mathematics
A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya
A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya
Publications
The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schrödinger 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.
Remling's Theorem On Canonical Systems, Keshav R. Acharya
Remling's Theorem On Canonical Systems, Keshav R. Acharya
Publications
In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the Hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system.