Schrödinger operators with singular potentials from the space of multiplicators
type: Item
instance of: scholarly article
title: Schrödinger operators with singular potentials from the space of multiplicators
zbMATH Open document ID: 0991.47036
DOI: 10.1007/BF02674201
author: M. I. Neiman-Zade
author: A. A. Shkalikov
published in: Mathematical Notes
publication date: 2001-05-13T00:00:00Z
review text: Schrödinger operators \(-\Delta + Q\) are considered where \(Q\) is a multiplication operator by a generalized function \(q\). The following problems are studied. 1. What singular functions \(q\) do admit a well-defined operator \(-\Delta + q(x)\)? This leads to the question when a generalized function \(q\) is a multiplicator from \(H^1(R^n)\) to \(H^{-1}(R^n)\), i.e. when the multiplication by this function is a bounded operator from \(H^1\) to \(H^{-1}\). 2. If the operator \(-\Delta + q\) with a given singular potential \(q\) is well-defined, is it possible to approximate it by operators with smooth potentials so that the spectra of the approximating operators are close to the spectrum of \(-\Delta + q\)? The main results of the paper give answers to the questions mentioned. Also a generalization to the polyharmonic operator \((-\Delta)^n\) is given.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35B27
zbMATH DE Number: 1517555
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: singular potential
zbMATH Keywords: generalized function
zbMATH Keywords: polyharmonic operator
zbMATH Keywords: Laplace operator
reviewed by: Milan Kučera
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02674201
OpenAlex ID: W2074809607
description: scientific article; zbMATH DE number 1517555