On essential self-adjointness of powers and comparison algebras
type: Item
instance of: scholarly article
title: On essential self-adjointness of powers and comparison algebras
zbMATH Open document ID: 0818.47016
DOI: 10.1007/BF02790358
published in: Journal d'Analyse Mathématique
publication date: 1994-09-19T00:00:00Z
review text: A class of second order elliptic differential operators \(L\) of Schrödinger type on a noncompact Riemannian manifold is considered. Let \(L_ 0\) be the corresponding minimal operator in the Hilbert space \(L^ 2\). Under some conditions the author proves that the operators \(L^ m_ 0\), \(m= 1,2,\dots\) are essentially self-adjoint. This fact is used in studying the corresponding comparison algebras. The case of the operator, \(L= -\partial^ 2+ q(q+ 1)x^{-2}\) on the half-line \((0,\infty)\), \(q\in \mathbb{R}\), is investigated in details.
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 640332
zbMATH Keywords: essentially self-adjoint elliptic operators
zbMATH Keywords: comparison algebras
zbMATH Keywords: second order elliptic differential operators
zbMATH Keywords: noncompact Riemannian manifold
zbMATH Keywords: minimal operator
author: Heinz Cordes
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 640332