Self-adjoint domains, symplectic geometry, and limit-circle solutions
type: Item
instance of: scholarly article
title: Self-adjoint domains, symplectic geometry, and limit-circle solutions
zbMATH Open document ID: 1262.34030
author: Siqin Yao
author: Jiong Sun
author: Anton Zettl
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-11-22T00:00:00Z
review text: Everitt and Markus characterized the domains of self-adjoint operator realizations of very general even- and odd-order symmetric ordinary differential equations in terms of Lagrangian subspaces of symplectic spaces. Recently, for the even-order case with real coefficients, Wang, Sun and Zettl constructed limit-circle (LC) solutions and Hao, Wang, Sun and Zettl characterized the self-adjoint domains in terms of LC solutions. These LC solutions are higher-order analogues of the celebrated Titchmarsh-Weyl limit-circle solutions in the second-order case. This LC characterization has been used to obtain information about the discrete, continuous, and essential spectra of these operators. In this paper, the authors investigate the connection between these two very different kinds of characterizations and thus add the methods of symplectic geometry to the techniques available for the investigation of the spectrum of self-adjoint operators.
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 6109988
zbMATH Keywords: self-adjoint differential operators
zbMATH Keywords: symplectic geometry
zbMATH Keywords: Lagrangian subspaces
zbMATH Keywords: limit-circle solutions
zbMATH Keywords: boundary conditions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.07.066
OpenAlex ID: W2075551842
DOI: 10.1016/J.JMAA.2012.07.066
description: scientific article; zbMATH DE number 6109988