The discrete spectrum in the gaps of a second-order perturbed periodic operator
type: Item
instance of: scholarly article
title: The discrete spectrum in the gaps of a second-order perturbed periodic operator
zbMATH Open document ID: 0733.35083
DOI: 10.1007/BF01079605
publication date: 1991-01-01T00:00:00Z
review text: The author studies perturbations of the Schrödinger operator by a potential which leads to a discrete spectrum in ``continuous gaps''. There are investigated the properties of the spectrum of the operator on \(L_ 2({\mathbb{R}}^ d)\), \(d\geq 3\), generated by \(-div(a(x)\text{grad} u)+f(x)u,\) where a(x) is \(C^ 1\) and the potential \(f\in L_{\infty}\) is real and periodic. In the case of regular perturbations there are described integral representations for some functionals defined in terms of eigenvalues of perturbation operators and gaps in the spectrum. There is also discussed the case of irregular perturbations.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 4212632
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: discrete spectrum
zbMATH Keywords: perturbations
zbMATH Keywords: gaps
author: M. Sh. Birman
MaRDI profile type: Publication
cites work: Q3972380
cites work: Q5749714
cites work: Q3972381
cites work: On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator HW in a spectral gap of H.
cites work: Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
cites work: Q5758528
full work available at URL: https://doi.org/10.1007/bf01079605
OpenAlex ID: W1996820666
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4212632