A limiting absorption principle for Schrödinger operators with oscillating potentials. Part I: \(-\Delta +c \sin(b| x|^{\alpha})/| x|^{\beta}\) for certain c,\(\alpha\),\(\beta\)
type: Item
instance of: scholarly article
title: A limiting absorption principle for Schrödinger operators with oscillating potentials. Part I: \(-\Delta +c \sin(b| x|^{\alpha})/| x|^{\beta}\) for certain c,\(\alpha\),\(\beta\)
zbMATH Open document ID: 0537.34024
DOI: 10.1016/0022-0396(83)90019-0
author: Allen Devinatz
author: Peter Rejto
published in: Journal of Differential Equations
publication date: 1983-01-01T00:00:00Z
review text: This paper presents a limiting absorption principle for Schrödinger operators with an oscillating potential of the form \(p_ 0(x)=c \sin(b| x|^{\alpha})/| x|^{\beta}, \alpha,\beta>0\). The main step in obtaining a limiting principle for \(H(p_ 0)=-\Delta +p_ 0(x)\) is to prove an important inequality. As the potential \(p_ 0(x)\) is radially symmetric the Schrödinger operator for this potential is unitarily equivalent to a direct sum of ordinary second order differential operators. Then, the approach is to replace the potentials by more easily handled approximating potentials. The details of proofs are given.
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 3853520
zbMATH Keywords: limiting absorption principle
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: oscillating potential
zbMATH Keywords: second order differential operators
reviewed by: J.-L.Guiraud
MaRDI profile type: Publication
full work available at URL: 0022-0396(83)90019-0
OpenAlex ID: W1984971947
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description: scientific article; zbMATH DE number 3853520