The pseudodifferential operator \(A(x,D)\)
type: Item
instance of: scholarly article
title: The pseudodifferential operator \(A(x,D)\)
zbMATH Open document ID: 1083.46022
DOI: 10.1155/S0161171204212388
author: Niranjan Chakravarthy
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/52189
review text: Summary: The pseudodifferential operator (p.d.o.) \(A(x,D)\), associated with the Bessel operator \(d^2/dx^2+(1-4\mu^2)/4x^2\), is defined. The symbol class \(H^{m}_{\rho,\delta}\) is introduced. It is shown that the p.d.o.\ associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space \(H_\mu\) into itself. An integral representation of the p.d.o.\ is obtained. Using the Hankel convolution, \(L^{p}_{\sigma,\alpha}\)-norm continuity of the p.d.o.\ is proved.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47G30
zbMATH DE Number: 2168621
zbMATH Keywords: PsDO
zbMATH Keywords: Bessel operator
zbMATH Keywords: symbol class
zbMATH Keywords: Zemanian space
zbMATH Keywords: integral representation
zbMATH Keywords: Hankel convolution
zbMATH Keywords: norm continuity
MaRDI profile type: Publication
OpenAlex ID: W2114707174
description: scientific article; zbMATH DE number 2168621