Some properties of the pseudodifferential operator \(h_{\mu ,a}\)
type: Item
instance of: scholarly article
title: Some properties of the pseudodifferential operator \(h_{\mu ,a}\)
zbMATH Open document ID: 1126.35116
author: Pradip K. Pandey
author: R. S. Pathak
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-07-19T00:00:00Z
review text: The authors study pseudodifferential operators of the form \[ (h_{\mu,a}u)(x)= \int^\infty_0(x\xi)^{1/2}y_\mu(x\xi)a(x,\xi) (h_\mu u)(\xi)\,d\xi,\quad u\in H_\mu, \] where \(a\in{\mathcal C}^\infty(I\times I)\), \(I=(a,\infty)\), is the symbol of \(h_{\mu,a}\), \(h_\mu\) denotes the Hankel transformation and \(H_\mu\) is the Zemanian space. They prove that the kernel of \(h_{\mu,a}\) is a continuous function and \(h_{\mu,a}\) is pseudolocal. A global regularity result for an elliptic partial differential operator is obtained and an existence theorem for the weak solution of a pseudodifferential equation is established.
reviewed by: Viorel Iftimie
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 5172995
zbMATH Keywords: Hankel transform
zbMATH Keywords: Hankel potential
zbMATH Keywords: pseudolocal
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.01.096
OpenAlex ID: W2043989298
cites work: Applications of analysis on nilpotent groups to partial differential equations
cites work: Integral Equations Associated with Hankel Convolutions
cites work: Q3736112
cites work: Hypoelliptic differential operators
cites work: Pseudo‐differential operators
cites work: Q5552928
cites work: The Complex Hankel andI-Transformations of Generalized Functions
cites work: Q4348658
cites work: A class of pseudo-differential operators associated with Bessel operators
cites work: Sobolev type spaces associated with Bessel operators
cites work: Q3562067
cites work: Q4183808
cites work: Q4939441
cites work: Q3999473
cites work: Q5571178
DOI: 10.1016/J.JMAA.2006.01.096
description: scientific article; zbMATH DE number 5172995