Abstract
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 ℂ. This provides an alternative proof of the De Branges theorem that the canonical systems with tr H1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.
Highlights
This paper deals with the canonical systems of the following form: Ju (x) = zH (x) u (x), z ∈ C. (1) Here J = ( −1 0 )and H(x) is a 2 × 2 positive semidefinite matrix whose entries are locally integrable
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 C
This provides an alternative proof of the De Branges theorem that the canonical systems with trH1 imply the limit point case
Summary
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 C. 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
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