An Alternate Proof of De Branges Theorem on Canonical Systems

2012/06/24 by Acharya, Keshav Raj
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1206.5550

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 H(x)=1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.

Related

• Canonical systems and de Branges spaces
• Inverse dynamic problems for canonical systems and de Branges spaces
• A growth estimate for the monodromy matrix of a canonical system
• Canonical systems with discrete spectrum
• Remling's Theorem on canonical systems