The essential self-adjointness of generalized Schrödinger operators
type: Item
instance of: scholarly article
title: The essential self-adjointness of generalized Schrödinger operators
zbMATH Open document ID: 0564.47010
DOI: 10.1016/0022-1236(85)90040-0
author: Norbert Wielens
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: The paper treats the essential self-adjointness of the generalized Schrödinger operator \[ A=-(1/2\rho)\sum^{n}_{i=1}D_ i(\rho D_ i) \] in the Hilbert space \(L^ 2(\Omega;\rho dx)\). In terms of related closed bilinear forms, a necessary and sufficient condition for the essential self-adjointness of \(A\) is given under general assumptions on \(\rho\) and for arbitrary domains \(\Omega\) in \({\mathbb{R}}^ n\). This criterion is used to prove that \(A\) is essentially self-adjoint in \(L^ 2({\mathbb{R}}^ n;\rho dx)\), if \(\rho\) is strictly positive and locally Lipschitz continuous on \({\mathbb{R}}^ n\). Furthermore, examples of non-essential self-adjointness and a complete discussion of the one dimensional case are included in the paper.
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 3899603
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Markovian extensions
zbMATH Keywords: uniqueness of Markov processes
zbMATH Keywords: weighted Sobolev spaces
zbMATH Keywords: essential self-adjointness of the generalized Schrödinger operator
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90040-0
OpenAlex ID: W2003300974
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description: scientific article; zbMATH DE number 3899603