On the localization of binding for Schrödinger operators and its extensions to elliptic operators
type: Item
instance of: scholarly article
title: On the localization of binding for Schrödinger operators and its extensions to elliptic operators
zbMATH Open document ID: 0859.35082
DOI: 10.1007/BF02788818
author: Yehuda Pinchover
published in: Journal d'Analyse Mathématique
publication date: 1997-04-09T00:00:00Z
review text: The lowest eigenvalue \(E(R)\) of perturbations of the \(n\)-dimensional Laplacian \(-\Delta+V(x)+W(x-R)\) is studied for large \(R\). The quantity is important in the discussion of the Efimov effect [\textit{H. Tamura}, J. Funct. Anal. 95, No.. 2, 433-459 (1991; Zbl 0761.35078)]. The main results are the bounds \(-C_1\leq R^{n-2}E(R)\leq-C_2\) in the case \(n\geq 5\) with assumptions on the decay of \(V\) and \(W\) which are in some sense optimal. The results are generalized to perturbations of equivariant operators for more general group actions on a manifold.
reviewed by: Joachim Asch
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 854437
zbMATH Keywords: perturbations of the Laplacian
zbMATH Keywords: Efimov effect
zbMATH Keywords: equivariant operators
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02788818
OpenAlex ID: W2330548359
description: scientific article; zbMATH DE number 854437