Spectral theory of magnetic Schrödinger operators with exploding potentials
type: Item
instance of: scholarly article
title: Spectral theory of magnetic Schrödinger operators with exploding potentials
zbMATH Open document ID: 0733.47008
author: Osanobu Yamada
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: Denote by H the (unique) selfadjoint extension of the Schrödinger operator \[ L=-\sum^{n}_{j=1}(\frac{\partial}{\partial x_ j}+ib_ j(x))^ 2+V(x), \] defined on \(C^{\infty}_ 0({\mathbb{R}}^ n)\), where the potential V is supposed to satisfy V(x)\(\to -\infty\) (\(| x| \to \infty)\) and \(V(x)\geq -C| x|^{\alpha}\) (\(| x| \geq R)\) for some \(\alpha <2\). The author studies conditions for the absolute continuity of H and derives its spectral representation. This continues previous work of Ikebe, Kato, Uchiyama, Eastham and Kalf.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 4212804
zbMATH Keywords: magnetic Schrödinger operators with exploding potentials
zbMATH Keywords: selfadjoint extension of the Schrödinger operator
zbMATH Keywords: absolute continuity
zbMATH Keywords: spectral representation
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519952
OpenAlex ID: W1510590857
DOI: 10.1215/KJM/1250519952
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description: scientific article; zbMATH DE number 4212804