Extensions, dilations and functional models of Dirac operators
type: Item
instance of: scholarly article
title: Extensions, dilations and functional models of Dirac operators
zbMATH Open document ID: 1088.47034
published in: Integral Equations and Operator Theory
publication date: 2005-06-16T00:00:00Z
review text: The author constructs a boundary value space for the Dirac operator in the limit-circle case. That leads to a description of various classes of extension of the minimal operator (selfadjoint, maximal dissipative, etc.) in terms of boundary conditions at \(\pm \infty\). Two classes of maximal dissipative extensions with separated boundary conditions (at \(+\infty\) and \(-\infty\)) are studied in detail. For each of them, the author constructs a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix within the scheme of Lax and Phillips. On the other hand, these constructions lead to functional models of the operators in question, the calculation of their characteristic functions, and completeness criteria for root vectors of maximal dissipative extensions. A similar program for the one-dimensional Schrödinger operator was implemented by the author and \textit{A.~Canoglu} in [Proc. R. Soc. Edinb., Sect. A, Math. 127, No.~6, 1113--1121 (1997; Zbl 0901.47001)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 2176369
zbMATH Keywords: Dirac operator
zbMATH Keywords: symmetric operator
zbMATH Keywords: maximal dissipative extension
zbMATH Keywords: boundary value space
zbMATH Keywords: characteristic function
zbMATH Keywords: scattering matrix
author: Bilender P. Allahverdiev
MaRDI profile type: Publication
full work available at URL: s00020-003-1241-0
OpenAlex ID: W2070557972
DOI: 10.1007/S00020-003-1241-0
description: scientific article; zbMATH DE number 2176369