An Alternate Proof of the De Branges Theorem on Canonical Systems. (3rd April 2014)

• Record Type: Journal Article
• Authors: Acharya, Keshav Raj
• Other Names: Karakostas G. L. Academic Editor.; Zhu C. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2014(2014)
• Publication Date: 2014-04-03
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.1155/2014/704607
• Languages: English
• ISSNs: 2090-4657

Abstract

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