Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 704607, 7 pages
http://dx.doi.org/10.1155/2014/704607
Research Article

An Alternate Proof of the De Branges Theorem on Canonical Systems

Department of Mathematics, Southern Polytechnic State University, 1100 South Marietta Pkwy, Marietta, GA 30060, USA

Received 21 December 2013; Accepted 18 March 2014; Published 3 April 2014

Academic Editors: G. L. Karakostas and C. Zhu

Copyright © 2014 Keshav Raj Acharya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 . This provides an alternative proof of the De Branges theorem that the canonical systems with imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.