Zhislin's theorem revisited
type: Item
instance of: scholarly article
title: Zhislin's theorem revisited
zbMATH Open document ID: 0808.35097
DOI: 10.1007/BF02790364
author: Roger T. Lewis
author: W. D. Evans
author: Yoshimi Saitō
published in: Journal d'Analyse Mathématique
publication date: 1995-03-05T00:00:00Z
review text: Zhislin's theorem gives a criterion for the atomic Schrödinger operator to have a finite number of bound states below its essential spectrum. Developing a general theory based on a function \(K\) introduced by S. Agmon (and which permits to study the operator in any given direction of the position space), the authors recover Zhislin's theorem as well as various other results concerning more general \((N+1)\)-body atomic-type operators. The theory is based on Sobolev-type and Hardy inequalities.
reviewed by: André Martinez
Mathematics Subject Classification ID: 35P99
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 640338
zbMATH Keywords: \(N\)-body Schrödinger operator
zbMATH Keywords: bound states
MaRDI profile type: Publication
cites work: Q3969238
cites work: Q3756011
cites work: The Oscillation of Elliptic Systems
cites work: N-Body Schrodinger Operators with Finitely Many Bound States
cites work: Some geometric spectral properties of N-body Schrödinger operators
cites work: Geometric spectral properties of N -body Schrödinger operators. II
cites work: On the Existence of Solutions of the Helium Wave Equation
cites work: Q4110164
cites work: Limits on stability of positive molecular ions
cites work: Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
cites work: Finiteness of the number of discrete eigenvalues of the Schrödinger operator for a three particle system
cites work: On the finiteness of discrete spectrum in the n-particle problem
cites work: Q3760977
cites work: ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR
cites work: SPECTRUM OF DIFFERENTIAL OPERATORS OF QUANTUM-MECHANICAL MANY-PARTICLE SYSTEMS IN SPACES OF FUNCTIONS OF A GIVEN SYMMETRY
description: scientific article; zbMATH DE number 640338