Self-adjointness of elliptic operators with infinitely many variables
type: Item
instance of: scholarly article
title: Self-adjointness of elliptic operators with infinitely many variables
zbMATH Open document ID: 0648.47035
DOI: 10.1007/BF01078432
author: N. N. Frolov
publication date: 1980-01-01T00:00:00Z
review text: The author studies the selfadjointness of infinite-dimensional differential operators of Schrödinger type. Let \({\mathcal L}u(x)=Lu(x)+p(x)u(x)\) be a differential operator on some Hilbert space, where L is a strongly symmetric infinite-dimensional differential operator on this Hilbert space [see the author, Mat. Zametki 24, no. 2, 241-248 (1978; Zbl 0414.47031)]. Of the function p assume that it is real-valued, measurable with respect to a Gaussian measure \(\mu\) and bounded on each bounded set of the Hilbert space under consideration. The results of this note are summarized in one theorem. In this theorem the author estalishes that if the operator \({\mathcal L}\) is bounded below then its closure is selfadjoint.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 35J99
zbMATH DE Number: 4058262
zbMATH Keywords: selfadjointness of infinite-dimensional differential operators of Schrödinger
zbMATH Keywords: Gaussian measure
zbMATH Keywords: bounded below
MaRDI profile type: Publication
cites work: Self-adjointness conditions for elliptic operators with infinitely many variables
cites work: Hypercontra ctive semigroups and two dimensional self-coupled Bose fields
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 4058262