Dissipative Schrödinger operators with matrix potentials
type: Item
instance of: scholarly article
title: Dissipative Schrödinger operators with matrix potentials
zbMATH Open document ID: 1048.34138
DOI: 10.1023/B:POTA.0000009815.97987.26
author: Bilender P. Allahverdiev
published in: Potential Analysis
publication date: 2004-03-15T00:00:00Z
review text: Lax-Phillips scattering theory and Nagy-Foias' theory of functional models are used for the study of the spectral properties of maximal dissipative extensions of the minimal operator \(L_{0}\) generated by the differential expression \(-y''(x)+Q(x)y(x)\) on \((-\infty,\infty)\). The matrix \(Q(x)\) is symmetric and its elements are real-valued and locally integrable on the real line. The author proves that almost all maximal dissipative extensions of \(L_0\) have purely discrete spectrum included in the open upper half-plane and that the system of eigenvectors and associated vectors of these extensions is complete.
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34L25
zbMATH DE Number: 2057483
zbMATH Keywords: maximal dissipative operator
zbMATH Keywords: scattering matrix
zbMATH Keywords: functional model
zbMATH Keywords: characteristic function
zbMATH Keywords: completeness of eigenvectors and associated vectors
zbMATH Keywords: selfadjoint dilation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2057483