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Full-Text Articles in Physical Sciences and Mathematics
An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya
An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya
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The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on ₵. This provides an alternative proof of the De Branges theorem that the canonical systems with trH1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.
Titchmarsh-Weyl Theory For Canonical Systems, Keshav R. Acharya
Titchmarsh-Weyl Theory For Canonical Systems, Keshav R. Acharya
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The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this end, we first observe the fact that Schrodinger and Jacobi equations can be written into canonical systems. We then discuss the theory of Weyl m-function for canonical systems and establish the relation between the Weyl m-functions of Schrodinger equations and that of canonical systems which involve Schrodinger equations.