On the essential self-adjointness of pseudodifferential operators
type: Item
instance of: scholarly article
title: On the essential self-adjointness of pseudodifferential operators
zbMATH Open document ID: 0669.35115
author: M. Nagase
author: Tomio Umeda
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: A proof is sketched of the essential self-adjointness on the Schwartz space \({\mathcal S}\) of pseudo-differential operators with symbols in \(S^ m_{\lambda,\rho,\delta}\) class, where \(m>0\), \(0\leq \delta <\rho \leq 1\) and \(\lambda\) is a basic weight function in the sense of Kumanogo. The main result says: if p(x,\(\xi)\) satisfies \[ | D^{\alpha}_ x D^{\beta}_{\xi} p(x,\xi)| \leq C_{\alpha \beta}| p(x,\xi)+i| \lambda (x,\xi)^{-\rho | \alpha | +\delta | \beta |}, \] for all \(\alpha\), \(\beta\), then the operator \(p^ w(X,D)\) is essentially selfadjoint on \({\mathcal S}\).
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4096078
zbMATH Keywords: essential self-adjointness
zbMATH Keywords: Schwartz space
zbMATH Keywords: weight function
reviewed by: Jan Janas
MaRDI profile type: Publication
full work available at URL: pjaa.64.94
OpenAlex ID: W2010701626
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DOI: 10.3792/PJAA.64.94
description: scientific article; zbMATH DE number 4096078